Question

State the domain and range of both the function and the inverse function. f(x) = 8 x + 8 f -1(x) = Domain of f(x): Range of f(x): Domain of f -1(x): Range of f -1(x)

Answer 1

`f^(-1)(x) = (x+8)/(8)`

Domain of f(x): All real values.

Range of f(x): All real values.

Domain of f -1(x): All real values.

Range of f -1(x): All real values

Explanation:

We are given the following function:

`f(x) = 8x + 8`

Since it is a line, we have that both the domain is the range is the real set.

Inverse function:

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

Finding the inverse function:

Exchange x and y in the original function, and isolate y. So

Original

`y = 8x + 8`

Exchanging:

`x = 8y - 8`

Isolating y:

`8y = x + 8`

`y = (x+8)/(8)`

`f^(-1)(x) = (x+8)/(8)`