Question

What are the domain and range of the logarithmic function f(x) = log7x? Use the inverse function to justify your answers.

Answer 1

I hope this helps you

Answer 2

1. Find the inverse function:

`y=\log 7x,\\ 7x=e^y,\\ \\ x=(e^y)/(7).`

Rechange x and y, then:

`y=(e^x)/(7).`

The inverse function is

`f^(-1)(x)=(e^x)/(7).`

2. The domain of f(x) is the range of
`f^(-1)(x)` and the range of f(x) is the domain of
`f^(-1)(x).`

3. The domain of
`f^(-1)(x)` is
`x\in (-\infty,\infty)` and the range of
`f^(-1)(x)` is
`y\in (0,\infty)`.

Answer: the domain of f(x) is
`x\in (0,\infty)` and the range of f(x) is
`y\in (-\infty,\infty).`