Quantitative Aptitude – Algebra – Functions – Let f(x) = 2x-5 and g(x) = 7-2x

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Functions - Let f(x) = 2x-5 and g(x) = 7-2x
Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

A) 5/2 < x < 7/2
B) x ≤ 5/2 or x ≥ 7/2
C) x < 5/2 or x ≥ 7/2
D) 5/2 ≤ x ≤ 7/2

Answer

Option (D)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
|f(x) + g(x)| = |f(x)| + |g(x)|
Putting value of f(x) and g(x), we get,
|2x-5| + |7-2x| = 2

1st Case: When x<=5/2
-2x + 5 +7 – 2x = 2
=> x=5/2

2nd Case: 5/2 < x < 7/2
On solving, we get, 2=2, which satisfies the condition

3rd Case: x ≥ 7/2
2x-5 – 7+2x = 2
x=7/2
So, the answer should be 5/2<= x <= 7/2
Option (D)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q2: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q3: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
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Quantitative Aptitude – Algebra – Functions – Let f(x) = 2x-5 and g(x) = 7-2x
5 (100%) 56 votes

Quantitative Aptitude – Algebra – Functions – If f(ab) = f(a)f(b) for all positive

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Functions - If f(ab) = f(a)f(b) for all positive
If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is

Answer

1

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
Let us take the case when a=b=1
So, f(1) = f(1) f(1)
f(1) = [f(1)]^2
f(1)[f(1)-1] = 0
f(1) = 1
So, the maximum value of f(1) = 1
Answer: 1

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q3: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

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a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Know More about Online CAT Course

Quantitative Aptitude – Algebra – Functions – If f(ab) = f(a)f(b) for all positive
5 (100%) 52 votes

Quantitative Aptitude – Algebra – Functions – Let f(x) = x^2 and g(x) = 2^x

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Functions - Let f(x) = x^2 and g(x) = 2^x
Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

A) 16
B) 18
C) 36
D) 40

Answer

Option (C)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
f(g(x)) = 2^(2x)
g(f(x)) = 2^((x)^2)
f(f(g(x)) + g(f(x)) = (2^(2x) + 2^(x^2))^2
at x = 1, we get 36
Option (C)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

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a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
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Quantitative Aptitude – Algebra – Functions – Let f(x) = x^2 and g(x) = 2^x
5 (100%) 52 votes

Quantitative Aptitude – Algebra – Functions – If f(x) = (5x+2)/(3x-5)

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)(3x-5)
If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is

A) 2
B) 1/3
C) 6
D) 2/3

Answer

Option (A)

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
f(3) = 17/4
f(17/4) = 3
g(3) = 2
Option (A)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

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a) 750+ Videos covering entire CAT syllabus
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c) Study Material & PDFs for practice and understanding
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e) Previous Year Questions solved on video

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Quantitative Aptitude – Algebra – Functions – If f(x) = (5x+2)/(3x-5)
5 (100%) 57 votes

Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - If f1(x) = x^2 + 11x + n
If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is

Answer

24

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,
f1(x) = f2(x)
x^2 + 11x +n = x
x^2 + 10x + n =0
To have distinct and real roots, D>0
D = b^2-4ac = 100 – 4n > 0
On solving the inequality, we get, n<25 So, max positive integer value of n = 24. Answer: 24

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q5: The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

Other posts related to Quantitative Aptitude – Algebra

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How to Solve Number of Integral Solutions Questions for CAT 2017
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An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

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Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n
4.9 (98.79%) 66 votes

Quantitative Aptitude – Algebra – Functions – The area of the closed region

Quantitative Aptitude – Algebra – Functions

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Functions - The area of the closed region
The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

A) 4π
B) 4
C) 8
D) 2π

Answer

Option (C)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Algebra – Functions,
Remember the formula |x| + |y| = n
Here, area bounded by the region = 2n^2
In the question, n=2
So, area = 8
Option (C)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra – Functions

Quantitative Aptitude – Algebra – Functions – Q1: Let f(x) = 2x-5 and g(x) = 7-2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
Quantitative Aptitude – Algebra – Functions – Q2: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is
Quantitative Aptitude – Algebra – Functions – Q3: Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
Quantitative Aptitude – Algebra – Functions – Q4: If f(x) = (5x+2)/(3x-5) and g(x) = x^2 – 2x – 1, then the value of g(f(f(3))) is
Quantitative Aptitude – Algebra – Functions – Q5: If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam​​

Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

Quantitative Aptitude – Algebra – Functions – The area of the closed region
5 (100%) 55 votes