# Test: Functions III - Challenging

Double click on maths expressions to zoom
Question 1:   Find the inverse function of $f\left(x\right)=x+2$
${f}^{-1}\left(x\right)=2x$
${f}^{-1}\left(x\right)=\frac{1}{x}+2$
${f}^{-1}\left(x\right)=x-2$
${f}^{-1}\left(x\right)=\frac{1}{x}-2$
Question 2:   Find the inverse function of$f\left(x\right)=\frac{x+2}{x-2}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x}$
${f}^{-1}\left(x\right)=2\frac{x-1}{x+1}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x-2}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x-1}$
Question 3:   Find the inverse function of $f\left(x\right)=\frac{3\left(x-5\right)}{2\left(x+1\right)}$
${f}^{-1}\left(x\right)=\frac{2x+15}{3-2x}$
${f}^{-1}\left(x\right)=\frac{2x+15}{2x-3}$
${f}^{-1}\left(x\right)=\frac{2x-15}{2x-3}$
${f}^{-1}\left(x\right)=\frac{2x+15}{2x+3}$
Question 4:   Find ${f}^{-1}\left(4\right)$ of $f\left(x\right)=\frac{2x-1}{5-3x}$
$\frac{1}{2}$
$\frac{3}{2}$
$-1$
$1$
Question 5:   If $f\left(x\right)=2x+1$ and $g\left(x\right)=\frac{1}{2}x-1$, find $f\left(g\left(x\right)\right)$
$f\left(g\left(x\right)\right)=2\frac{1}{2}x$
$f\left(g\left(x\right)\right)=x-1$
$f\left(g\left(x\right)\right)=2x+2$
$f\left(g\left(x\right)\right)={x}^{2}-1$
Please note, you have solved only half of the test. For the complete test get a Must Have account. Get started