Question

Let f(x) = 2x² - 8 and let g(x) = 3x + 1. Find the given value.f[g(-2)]f[g(-2)]= (Type an integer or a decimal.)

Answer 1

f[g(-2)] = 42

Explanation

To find f[g(-2)], first, we need to find g(-2).

To find g(-2) we have to substitute x = -2 into the function g(x), as follows:

`\begin{gathered} g(x)=3x+1 \\ g(-2)=3\cdot(-2)+1 \\ g(-2)=-6+1 \\ g(-2)=-5 \end{gathered}`

In consequence, f[g(-2)] is equivalent to:

`f\lbrack g(-2)]=f(-5)`

To find f(-5) we have to substitute x = -5 into the function f(x), as follows:

`\begin{gathered} f(x)=2x^2-8 \\ f(-5)=2(-5)^2-8 \\ f(-5)=2\cdot25-8 \\ f(-5)=50-8 \\ f(-5)=42=f\lbrack g(-2)] \end{gathered}`