CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 22 : If \(f(x)=x^{2}-7 x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))-3 x\) is

Video Explanation

Explanatory Answer

g(x) = x + 3
f(x) = x² - 7x
f(g(x)) - 3x
= f(x + 3) - 3x
= (x + 3)² - 7(x + 3) - 3x
= x² + 9 + 6x - 7x - 21 - 3x
= x² - 4x - 12
= x² - 4x + 4 - 4 - 12
= x² - 4x + 4 - 16
= (x - 2)² - 16
f(g(x)) - 3x is minimum when (x - 2)² - 16 is minimum.
(x - 2)² - 16 is minimum when (x - 2)² is minimum.
Since (x - 2)² is non-negative, the minimum value it can take is 0.
Hence the minimum value of (x - 2)² - 16 = 0 - 16 = -16
Therefore, the minimum value of f(g(x)) - 3x is -16

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

Hence, the answer is '- 16'

Choice D is the correct answer.

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