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