Question: Let \( f(x) = 5x - 8 \). Find \( (f \circ f)(6) \). \( (f \circ f)(6) =…

Let \( f(x) = 5x - 8 \). Find \( (f \circ f)(6) \).

\( (f \circ f)(6) = \boxed{\phantom{0}} \)

(Simplify your answer.)

Solution

The problem is asking to find \((f \circ f)(6)\), where \(f(x) = 5x - 8\). First, we need to find \(f(6)\). \[ f(6) = 5(6) - 8 \] Calculate: \[ f(6) = 30 - 8 = 22 \] Next, find \(f(f(6))\) which is \(f(22)\). Substitute \(x = 22\) into the function \(f(x)\): \[ f(22) = 5(22) - 8 \] Calculate: \[ f(22) = 110 - 8 = 102 \] So, \((f \circ f)(6) = 102\).