Quantitative Aptitude - Algebra - Functions - If f(ab) = f(a)f(b) for all positive
Quantitative Aptitude - Algebra - Functions
Question
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
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Quantitative Aptitude - Algebra - Functions - Let f(x) = x^2 and g(x) = 2^x
Quantitative Aptitude - Algebra - Functions
Question
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)
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Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)/(3x-5)
Quantitative Aptitude - Algebra - Functions
Question
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)
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Quantitative Aptitude - Algebra - Functions - If f1(x) = x^2 + 11x + n
Quantitative Aptitude - Algebra - Functions
Question
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
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Quantitative Aptitude - Algebra - Functions - The area of the closed region
Quantitative Aptitude - Algebra - Functions
Question
The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
A) 4Ï€
B) 4
C) 8
D) 2Ï€
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)
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Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2}
Slot -2 – Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2}
 Let f(x)=max{5x, 52-2x^2}, where x is any positive real number. Then the minimum possible value of f(x) is?
Answer: 20
Solution:
For f(x) to be minimum , 5 = 52 − 2^2
2^2+5 −52 =0
−42+13=0
= 4
Thus minimum value of f(x) = 5x = 5*4 = 20
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Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1)
Slot -1 – Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1)
 If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals?
Answer: 54
Solution:
Given , f(x + 2) = f(x) + f(x + 1)
f(15) = f(13) + f(14)
f(13) + f(14) = 617 ---------------1)
f(12) + f(13) = f(14) -------------2)
f(11) + f(12) = f(13)-------------3)
from eq 1) , 2) & 3)
2f(11) + 3f(12) =
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Quantitative Aptitude – Algebra - Functions – Let f(x) = min{2x^2,52−5x}
Slot -1 – Quantitative Aptitude – Algebra - Functions – Let f(x) = min{2x2,52−5x}
Let f(x) = min{2x2,52−5x}, where x is any positive real number. Then the maximum possible value of f(x) is ( TITA )?
Answer: 32
Solution: for maximum possible value , 2x2= 52−5x
2x2+ 5x – 52 = 0
(x -4)*(x+6.5) = 0
So x = 4 ( as x is positive real number )
Maximum possible value of f(x) = 2x2= 52−5x = 32
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