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CAT 2021 Slot 3 QA Question & Solution

AlgebraMedium

Question

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

Options

-20
-12
-15
-16

Solution

Now we have :
$f(g(x))-3x$
so we get f(x+3)-3x
= $\left(x+3\right)^2-7\left(x+3\right)-3x$
=$x^2-4x-12$
Now minimum value of expression = $-\frac{D}{4a}$ $\frac{\left(4ac-b^2\right)}{4a}$
We get: $\quad$- (16+48)/4
$\Rightarrow$ -16