Answer
(a) The graph is shown in the image below. It is symmetric about the origin.
(b) $f$ is its own inverse. To prove that, find the inverse of function $f(x)=\frac{1}{x}$ like normal.
Work Step by Step
(a) The graph of function $f(x)=\frac{1}{x}$ is shown in the image below.
The graph, as we can see, is symmetric about the origin.
(b) To see if the function $f(x)=\frac{1}{x}$ is its own inverse or not, we would find the inverse of $f(x)=\frac{1}{x}$
- First, solve for $x$ in terms of $f(x)$:
$$f(x)=\frac{1}{x}$$
$$x=\frac{1}{f(x)}$$
- Now, interchange $x$ and $f(x)$:
$$f^{-1}(x)=\frac{1}{x}$$
As you can see, both the function and its inverse are the same.
Therefore, $f$ is its own inverse.
