CAT 2021 Question Paper | CAT Verbal Ability Slot 3
Question :
Started 2 weeks ago by Shashank in
Option A
is the correct answer.
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
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