Question

F(x) = 8x - 7 and g(x) = x 7/8 answer two questions about these functions. write a simplified expression for g(f(x)) in terms of x.

Answer 1

To find g(f(x)), we substitute f(x) into g(x), resulting in the expression (8x - 7)^(7/8), which cannot be further simplified. This final expression represents the composition of the two functions.

Step-by-step explanation:

To find a simplified expression for g(f(x)) in terms of x, we need to plug the function f(x) into g(x). The given functions are f(x) = 8x - 7 and g(x) = x + ·/8. Since the question seems to have a typo in g(x), we will correct it and assume g(x) = x^(7/8), which is a common type of function involving fractional exponents.

First, we compute f(x): f(x) = 8x - 7. Next, we replace x in g(x) with f(x): g(f(x)) = (8x - 7)^(7/8). There are no like terms to combine or further simplifications that can be applied to this expression, so this is our final simplified expression for g(f(x)).

Here's the process step by step:

1. Identify the inner function f(x) and the outer function g(x).
2. Compute f(x): f(x) = 8x - 7.
3. Substitute f(x) into g(x): g(f(x)) = (8x - 7)^(7/8).
4. Realize that the expression cannot be further simplified.