Answer: \(f(g(x)) = 12x + 26\)
Explanation:
To find \(f(g(x))\), you'll first substitute the expression for \(g(x)\) into \(f(x)\). Here are the steps:
1. Start with \(f(x)\):
\[f(x) = 6x - 4\]
2. Now, substitute \(g(x)\) into \(f(x)\):
\[f(g(x)) = 6(g(x)) - 4\]
3. Replace \(g(x)\) with its expression:
\[f(g(x)) = 6(2x + 5) - 4\]
4. Distribute the 6 into the terms inside the parentheses:
\[f(g(x)) = 12x + 30 - 4\]
5. Simplify the expression:
\[f(g(x)) = 12x + 26\]
So, \(f(g(x)) = 12x + 26\).