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:

$y=\log 7x,\\ 7x=e^y,\\ \\ x=\dfrac{e^y}{7}.$

Rechange x and y, then:

$y=\dfrac{e^x}{7}.$

The inverse function is

$f^{-1}(x)=\dfrac{e^x}{7}.$

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 $y\in (-\infty,\infty).$