**Quantitative Aptitude – Algebra – Functions**

**Question**

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

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