CAT 2021 Slot 3 QA Q22 Functions & Graphs

Question 22 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

If \(f(x)=x^{2}-7 x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))-3 x\) is

A
- 20
B
- 15
C
- 12
D
- 16

Answer: (D) - 16 Functions & Graphs MCQ

Solution

\(f(g(x)) = (x+3)^2 - 7(x+3) = x^2 - x - 12\).
\(f(g(x)) - 3x = x^2 - 4x - 12 = (x - 2)^2 - 16\).
Minimum \(= -16\) at \(x = 2\).