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, 6, right parenthesis, .(g∘f)(6).
f, of, x, equals, x, minus, 6
f(x)=
x−6
g, of, x, equals, 2, x, squared, minus, 2, x, plus, 12
g(x)=
2x
2
−2x+12

Answer 1

To find \((g \circ f)(6)\), we need to evaluate \(f(6)\) first and then substitute that result into \(g(x)\).

1. **Calculate \(f(6)\)**:
\[
f(x) = x - 6
\]
Substitute \(x = 6\):
\[
f(6) = 6 - 6 = 0
\]

2. **Now calculate \(g(f(6))\), which is \(g(0)\)**:
\[
g(x) = 2x^2 - 2x + 12
\]
Substitute \(x = 0\):
\[
g(0) = 2(0)^2 - 2(0) + 12 = 0 - 0 + 12 = 12
\]

Therefore, the value of \((g \circ f)(6)\) is \(\boxed{12}\).