Explanation:
To find g(f(x)), you need to first substitute the expression for f(x) into g(x). Here are the steps:
1. Start with the expression for g(x):
g(x) = 2x + 12
2. Now, replace x in g(x) with the expression for f(x):
g(f(x)) = 2f(x) + 12
3. The expression for f(x) is:
f(x) = 2x^2 - x + 6
4. Substitute this into g(f(x)):
g(f(x)) = 2(2x^2 - x + 6) + 12
5. Distribute the 2 on the right side of the equation:
g(f(x)) = 4x^2 - 2x + 12 + 12
6. Combine like terms:
g(f(x)) = 4x^2 - 2x + 24
So, g(f(x)) is equal to 4x^2 - 2x + 24.