cat 2021 Question 22

Question

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

Accepted Answer

Now we have:

$f(g(x))−3x$

so we get $f(x+3)-3x$

= $(x+3)^2 - 7(x+3) - 3x$

= $x^2 - 4x - 12$

Now minimum value of expression = $-\frac{D}{4a}\frac{4ac-b^2}{4a}$

We get - $(16+48)/4$ = -16

Question 22.