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).

Question

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 \(\boxed{5}\).