Question

Find f(g(2)) for the following:Given: F(x) = 2x^2 - 1, g(x) =x+2Find: f(g(2))

Answer 1

$f(g(2))=31$

Explanation

Step 1

Let

$\begin{gathered} f(x)=2x^2-1 \\ g(x)=x+2 \\ \end{gathered}$

a) find g(2), to do that, replace the given value in the x place

so

$\begin{gathered} g(x)=x+2 \\ \text{when x=2} \\ g(2)=2+2 \\ g(2)=4 \end{gathered}$

b)now f(g(2))

now, evaluate f(x) for the previous answer,so

$\begin{gathered} f(x)=2x^2-1 \\ f\mleft(g\mleft(2\mright)\mright)=2(4)^2-1 \\ f\mleft(g\mleft(2\mright)\mright)=32-1 \\ f(g(2))=31 \end{gathered}$

so, the answer is

f(g(2))=31

I hope this helps you