Question

question
given the definitions of $f(x)$ and $g(x)$ below, find the value of $(g \circ f)(-2)$.
$f(x) = 2x^2 - 3x - 10$
$g(x) = 4x - 11$

Explanation:

Step1: Find f(-2)

First, we need to find the value of \( f(-2) \) by substituting \( x = -2 \) into the function \( f(x) = 2x^2 - 3x - 10 \).

\[

$$\begin{align*} f(-2) &= 2(-2)^2 - 3(-2) - 10 \\ &= 2(4) + 6 - 10 \\ &= 8 + 6 - 10 \\ &= 4 \end{align*}$$

\]

Step2: Find (g ∘ f)(-2) which is g(f(-2))

Now that we know \( f(-2) = 4 \), we substitute this value into the function \( g(x) = 4x - 11 \) to find \( g(4) \).

\[

$$\begin{align*} g(4) &= 4(4) - 11 \\ &= 16 - 11 \\ &= 5 \end{align*}$$

\]

Answer:

\( 5 \)