Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 20: Exercise 3H

Find $f^{-1}\left(x\right)$ for the linear function $f\left(x\right)=-3x+9$. Give your answers in the form $f^{-1}\left(x\right) = mx + c$$$

Find $f^{-1}\left(x\right)$ for the linear function $f\left(x\right)=4x-5$. Give your answers in the form $f^{-1}\left(x\right) = mx + c$.

Find $f^{-1}\left(x\right)$ for the linear function $f\left(x\right)=-\frac{1}{6}x+3$. Give your answers in the form $f^{-1}\left(x\right) = mx + c$.

Find $f^{-1}\left(x\right)$ for the linear function $f\left(x\right)=0.25x+1.75$. Give your answers in the form $f^{-1}\left(x\right) = mx + c$.

The graph of a linear function $y=f\left(x\right)$ and the line $y=x$ is shown below. Copy the graphs and then add a sketch of the graph of $y=f^{-1}\left(x\right)$.

A t-shirt company imprints logos on t-shirts. The company charges a one-time set-up fee of $\$65$ and $\$10$ per shirt. The total cost of $x$ shirts, in $\mathrm{CAD}$, is given by $f\left(x\right) = 10x + 65$. Find the total cost for $55$ t-shirts.

A t-shirt company imprints logos on t-shirts. The company charges a one-time set-up fee of $\$65$ and $\$10$ per shirt. The total cost of $x$ shirts, in $\mathrm{CAD}$, is given by $f\left(x\right) = 10x + 65$. Find $f^{-1}\left(x\right)$ and tell what $x$ and $f^{-1}\left(x\right)$ represent in this function.