Question

If f(x)=3x^2-2, find h(x)

Answer 1

Given

$f(x)=3x^2-2$$h(x)\text{ = f(x+5) -2}$

Let us find f(x+5)

$\begin{gathered} f(x+5)=3(x+5)^2-\text{ 2} \\ =\text{ 3(x+5)(x+5) - 2} \\ =3(x^2+5x+5x+25)-2 \\ =3(x^2+10x+25)\text{ - 2} \\ =3x^2+30x+75-2_{} \\ =3x^2+30x+73 \end{gathered}$

To find h(x)= f(x+5) - 2, we substitute for f(x+5)

Then, we have

$\begin{gathered} h(x)=3x^2+30x+73\text{ - 2} \\ h(x)=3x^2+30x+71 \end{gathered}$

The answer to the function h(x) is 3x²+30x+71