Question: Let \( f(x) = 2x + 5 \) and \( g(x) = 3x^2 - 3 \). Evaluate \( (f \circ g)(2) \). \( (f…

Let \( f(x) = 2x + 5 \) and \( g(x) = 3x^2 - 3 \). Evaluate \( (f \circ g)(2) \).

\( (f \circ g)(2) = \boxed{\phantom{0}} \) (Simplify your answer.)

Solution

To evaluate \((f \circ g)(2)\), we follow these steps: First, find \(g(2)\). \[ g(x) = 3x^2 - 3 \] Substitute \(x = 2\): \[ g(2) = 3(2)^2 - 3 \] \[ g(2) = 3(4) - 3 \] \[ g(2) = 12 - 3 \] \[ g(2) = 9 \] Next, use this result to find \(f(g(2)) = f(9)\). \[ f(x) = 2x + 5 \] Substitute \(x = 9\): \[ f(9) = 2(9) + 5 \] \[ f(9) = 18 + 5 \] \[ f(9) = 23 \] Therefore, \((f \circ g)(2) = 23\).