Question

question given the definitions of f(x) and g(x) below, find the value of (g∘f)(-2). f(x) = 2x² - 3x - 10 g(x) = 4x - 11 answer attempt 1 out of 2 submit answer

Explanation:

Step1: Find \( f(-2) \)

Substitute \( x = -2 \) into \( f(x) = 2x^2 - 3x - 10 \).
\[

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

\]

Step2: Find \( (g \circ f)(-2) = g(f(-2)) \)

Since \( f(-2) = 4 \), substitute \( x = 4 \) into \( g(x) = 4x - 11 \).
\[

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

\]

Answer:

\( 5 \)