1. Find the inverse function:
[tex] y=\log 7x,\\ 7x=e^y,\\ \\ x=\dfrac{e^y}{7}.[/tex]
Rechange x and y, then:
[tex] y=\dfrac{e^x}{7}.[/tex]
The inverse function is
[tex] f^{-1}(x)=\dfrac{e^x}{7}.[/tex]
2. The domain of f(x) is the range of [tex] f^{-1}(x)[/tex] and the range of f(x) is the domain of [tex] f^{-1}(x).[/tex]
3. The domain of [tex] f^{-1}(x)[/tex] is [tex] x\in (-\infty,\infty)[/tex] and the range of [tex] f^{-1}(x)[/tex] is [tex] y\in (0,\infty) [/tex].
Answer: the domain of f(x) is [tex] x\in (0,\infty) [/tex] and the range of f(x) is [tex] y\in (-\infty,\infty).[/tex]
