To find g(f(x)), we first need to determine what f(x) evaluates to given our function definition.
1. Start by calculating f(x):
- f(x) = (x – 5) / 8.
This means that for any value of x, f(x) gives us (x – 5) divided by 8.
2. Next, we plug f(x) into g(x):
- g(x) = 8x + 5.
Now, we replace x in g(x) with f(x):
- g(f(x)) = 8[f(x)] + 5 = 8[(x – 5) / 8] + 5.
3. Simplifying it:
- g(f(x)) = 8 * (x – 5) / 8 + 5.
- The 8s cancel out, so we are left with x – 5 + 5.
- This simplifies to x.
Thus, the result of g(f(x)) is simply:
- g(f(x)) = x.