Chapter 2.5, Problem 109E

Recall that the inverse of a function $f\left(x\right)$ is written as $f^{-1}\left(x\right)$ while the reciprocal of $f\left(x\right)$ can be written as either $\frac{1}{f\left(x\right)}$

or ${\left[f\left(x\right)\right]}^{-1}$

.The point of this exercise is to make clear that the reciprocal of a function has nothing to do with the inverse of a function. Let $f\left(x\right)=2x+3$. Find both ${\left[f\left(x\right)\right]}^{-1}$

and $f^{-1}\left(x\right)$. Compare the two functions. Graph all three functions on the same coordinate axes.