Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Relationships: Introducing Functions, Exercise 31: Exercise 2I

For the function below, using your $\mathrm{GDC}$, sketch its graph.

$f\left(x\right)=-4x^2+4,\text{ for }x\ge 0$

For the function below, using your $\mathrm{GDC}$, sketch its graph.

$g\left(x\right)=-2\sqrt{x}+5$

For the function below, using your $\mathrm{GDC}$, sketch its graph.

$g:x\to \frac{1}{2}x+6$

If $f\left(x\right)=2x-5$, solve $f\left(x\right)=11$.

If $f\left(x\right)=2x-5$, find $f^{-1}\left(11\right)$.

If $f\left(x\right)=2x-5$

What do you notice about your answers to parts $f\left(x\right)=11$ and $f^{-1}\left(11\right)$?

If $f\left(x\right)=2x-5$

Create a general rule to explain your answer for part $f\left(x\right)=11$ and $f^{-1}\left(11\right)$.

Given that $f\left(x\right)=-2x-1\text{ and }g\left(x\right)=-3x^2$, show that $g\circ f^{-1}(-1)=0$.