Question

Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, g, circle, f, right parenthesis, left parenthesis, minus, 2, right parenthesis, .(g∘f)(−2).
f, of, x, equals, 2, x, squared, minus, 3, x, minus, 10
f(x)=
2x
2
−3x−10
g, of, x, equals, 4, x, minus, 11
g(x)=
4x−11

Answer 1

To find \((g \circ f)(-2)\), we need to first evaluate \(f(-2)\) and then use that result to evaluate \(g(f(-2))\).

1. **Evaluate \(f(-2)\)**:
\[
f(x) = 2x^2 - 3x - 10
\]
Thus,
\[
f(-2) = 2(-2)^2 - 3(-2) - 10
\]
Calculating this step-by-step:
\[
= 2(4) + 6 - 10
\]
\[
= 8 + 6 - 10
\]
\[
= 4
\]

2. **Now evaluate \(g(f(-2))\), which is \(g(4)\)**:
\[
g(x) = 4x - 11
\]
Thus,
\[
g(4) = 4(4) - 11
\]
Calculating this:
\[
= 16 - 11
\]
\[
= 5
\]

Therefore, the value of \((g \circ f)(-2)\) is \(\boxed{5}\).