XAT 2015 Quant & DI: Functions

This aptitude practice question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. Question 11 of a total of 33 questions that appeared in this section in XAT 2015. This one is a medium level difficulty question and tests the concept of equating f(0) of a function given two instances of the function.

Question

If f(x² – 1) = x⁴ – 7x² + k₁ and f(x³ – 2) = x⁶ – 9x³ + k₂ then the value of (k₂ – k₁) is

1. 6
2. 7
3. 8
4. 9
5. None of the above

  Correct Answer      Choice C. The value of (k₂ – k₁) is 8

Explanatory Answer

Given Data

f(x² – 1) = x⁴ – 7x² + k₁

f(x³ – 2) = x⁶ – 9x³ + k₂

Approach and Solution

When x² = 1, f(x² – 1) = f(1 - 1) = f(0) =(1)² - 7(1) + k₁
f(0) = - 6 + k₁ ..........(1)
Essentially, we have replaced all x² with 1.

When x³ = 2,f(x³ – 2) = f(2 - 2) = f(0) =(2)² - 9(2) + k₂
f(0) = - 14 + k₂ ..........(2)
Essentially, we have replaced all x³ with 2.

Equating f(0) in equations (1) and (2)
(-6 + k₁) = (-14 + k₂)
or k₂ - k₁ = 8

  The correct answer is Choice C.

Video Explanation