Question

Given the functions f(x) = 2x + 4 and g(x) = 3x - 6, what is f(g(x)) when x = 6?

• A. 144
• B. 12
• C. 28
• D. 192
• E. 16

Hint:

For composite functions like \(f(g(x))\), always work from the inside out. First, evaluate the inner function \(g(x)\) for the given value, then plug that result into the outer function \(f(x)\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves the composition of two functions, denoted as \(f(g(x))\). This means we first evaluate the inner function, \(g(x)\), at the given value of \(x\), and then use that result as the input for the outer function, \(f(x)\).
Step 2: Detailed Explanation:
We are asked to find the value of \(f(g(x))\) when \(x = 6\).
First, we need to calculate \(g(6)\).
The function \(g(x)\) is given by \(g(x) = 3x - 6\).
Substitute \(x = 6\) into \(g(x)\):
\[ g(6) = 3(6) - 6 \] \[ g(6) = 18 - 6 \] \[ g(6) = 12 \] Now that we have the value of \(g(6)\), we use this result as the input for the function \(f(x)\).
We need to find \(f(g(6))\), which is \(f(12)\).
The function \(f(x)\) is given by \(f(x) = 2x + 4\).
Substitute \(x = 12\) into \(f(x)\):
\[ f(12) = 2(12) + 4 \] \[ f(12) = 24 + 4 \] \[ f(12) = 28 \] Step 3: Final Answer:
Therefore, the value of \(f(g(x))\) when \(x = 6\) is 28.