I have received this question for my homework, and I am quite unsure on how I should attempt to answer this. Can someone please explain how I can go about solving this?
Let $\:f : \Bbb R →]1, +∞[$ with $f(x) = 2^x + 1$.
(a) Find the inverse function
(b) Plot the curves of both functions, $f$ and $f^{-1}$ in the same graph.
(c) What can you say about these two curves?
If $y=f^{-1}(x)$, we get $x=f(y)$ . Find the inverse by interchanging $x$ and $y$ and solving for $y$.
To wit, we get $x=2^y+1$, and we solve for $y$. Get $2^y=x-1$. Now use $\ln$, say. Get $y=\dfrac {\ln(x-1)}{\ln2}$.
After plotting the two curves, you will notice that they are reflections of each other about the line $y=x$. (That's the effect of interchanging $x$ and $y$.)