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).

Question

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: \[ \boxed{53} \]