Question

Given the definitions of f, of, xf(x) and g, of, xg(x) below, find the value of left parenthesis, f, circle, g, right parenthesis, left parenthesis, 2, right parenthesis, .(f∘g)(2).
f, of, x, equals, x, squared, minus, 4, x, plus, 8
f(x)=
x
2
−4x+8
g, of, x, equals, 2, x, plus, 5
g(x)=
2x+5

Answer 1

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

1. Calculate \(g(2)\):
\[
g(x) = 2x + 5
\]
Substituting \(x = 2\):
\[
g(2) = 2(2) + 5 = 4 + 5 = 9
\]

2. Now that we have \(g(2) = 9\), we use this result to find \(f(g(2)) = f(9)\):
\[
f(x) = x^2 - 4x + 8
\]
Substituting \(x = 9\):
\[
f(9) = 9^2 - 4(9) + 8
\]
Calculate \(9^2\):
\[
9^2 = 81
\]
Calculate \(-4(9)\):
\[
-4(9) = -36
\]
Now substituting these values into the equation:
\[
f(9) = 81 - 36 + 8
\]
Combine the values:
\[
81 - 36 = 45
\]
\[
45 + 8 = 53
\]

Thus, \((f \circ g)(2) = f(g(2)) = f(9) = 53\).

Therefore, the final answer is:
\[
\boxed{53}
\]