CAT 2021 Functions Question (Hard)

Question

If and , then the minimum value of is

Accepted Answer

Step 1 We are given We need to compute the minimum value of Step 2 First, compute Then Expand So Now subtract Step 3 Minimize the expression This is a quadratic expression. Its minimum occurs at Substitute into the expression Final Answer The minimum value of is -16

CAT 2021

Quantitative

Functions

Hard

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

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