Answer
See explanation
Work Step by Step
(a)
$$y=\frac{1}{2}x-3$$
Exchange $x$ and $y$:
$$x=\frac{1}{2}y-3$$
Solve for $y$:
$$2(x+3)=y$$
$$y=2x+6$$
Replace $y$ by $f^{-1}(x)$:
$$f^{-1}(x)=2x+6$$
(b) The graph of $f$ and $f^{-1}$ is as shown.
(c) $f^{-1}$ is a reflection of $f$ across the line $y=x$.
(d) The domain of $f$ is all real numbers and its range is all real numbers, while the domain of $f^{-1}$ is all real numbers and its range is all real numbers.
