Question

Functions f and g are invertible functions. 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. g(f(x))Functions f and g are invertible functions. 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. g(f(x))

Answer 1

To find the simplified expression for g(f(x)), where f(x) = 8x - 7 and g(x) = (x + 7) / 8, we substitute f(x) into g, yielding g(f(x)) = x. This shows that g is the inverse function of f.

Step-by-step explanation:

The question asks for a simplified expression for g(f(x)), given that f(x) = 8x - 7 and g(x) = (x + 7) / 8. To find g(f(x)), we substitute f(x) into g where the x in g(x) would normally be. This means we will be evaluating g(8x - 7).

By substituting, we get:

g(f(x)) = g(8x - 7) = ((8x - 7) + 7) / 8 = 8x / 8 = x.

So, the simplified expression for g(f(x)) in terms of x is simply x. The composition of the two functions results in the identity function, meaning g is the inverse of f and vice versa.