# Test: Functions III - Challenging

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Question 1:   Find the inverse function of $f\left(x\right)=x+2$
${f}^{-1}\left(x\right)=\frac{1}{x}+2$
${f}^{-1}\left(x\right)=\frac{1}{x}-2$
${f}^{-1}\left(x\right)=x-2$
${f}^{-1}\left(x\right)=2x$
Question 2:   Find the inverse function of$f\left(x\right)=\frac{x+2}{x-2}$
${f}^{-1}\left(x\right)=2\frac{x-1}{x+1}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x-2}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x}$
${f}^{-1}\left(x\right)=\frac{2x+2}{x-1}$
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 $f\left(g\left(x\right)\right)$
$f\left(g\left(x\right)\right)=2\frac{1}{2}x$
$f\left(g\left(x\right)\right)=2x+2$
$f\left(g\left(x\right)\right)=x-1$
$f\left(g\left(x\right)\right)={x}^{2}-1$
Question 6:   If $f\left(x\right)=2x+1$ and $g\left(x\right)=\frac{1}{2}x-1$, find $g\left(f\left(x\right)\right)$
$g\left(f\left(x\right)\right)=x$
$g\left(f\left(x\right)\right)=x+\frac{1}{2}$
$g\left(f\left(x\right)\right)=x-1\frac{1}{2}$
$g\left(f\left(x\right)\right)=x-\frac{1}{2}$
Question 7:   If $f\left(x\right)=-2x-5$, $g\left(x\right)=\frac{1}{3}x+3$, $h\left(x\right)=5\left(x+1\right)$ find $f\left(g\left(h\left(x\right)\right)\right)$
$f\left(g\left(h\left(x\right)\right)\right)=3\frac{1}{3}x-\frac{2}{3}$
$f\left(g\left(h\left(x\right)\right)\right)=\frac{1}{3}x+\frac{2}{3}$
$f\left(g\left(h\left(x\right)\right)\right)=-1\frac{1}{3}x-2\frac{1}{6}$
$f\left(g\left(h\left(x\right)\right)\right)=-3\frac{1}{3}x-14\frac{1}{3}$
Question 8:   If $f\left(x\right)=-2x-5$, $g\left(x\right)=\frac{1}{3}x+3$, $h\left(x\right)=5\left(x+1\right)$ find $g\left(f\left(h\left(x\right)\right)\right)$
$g\left(f\left(h\left(x\right)\right)\right)=-3\frac{1}{3}x+\frac{1}{3}$
$g\left(f\left(h\left(x\right)\right)\right)=3\frac{1}{3}x+\frac{1}{3}$
$g\left(f\left(h\left(x\right)\right)\right)=-3\frac{1}{3}x-2$
$g\left(f\left(h\left(x\right)\right)\right)=3\frac{1}{3}x-\frac{1}{3}$
Question 9:   If $f\left(x\right)=-\frac{2}{5}x+7$, $g\left(x\right)=\frac{3}{2}x-1$ find $f{\left(g\left(x\right)\right)}^{-1}$
$f{\left(g\left(x\right)\right)}^{-1}=-\frac{2}{5}x+7\frac{1}{5}$
$f{\left(g\left(x\right)\right)}^{-1}=-\frac{3}{5}x+7\frac{2}{5}$
$f{\left(g\left(x\right)\right)}^{-1}=-\frac{1}{3}x+11\frac{2}{3}$
$f{\left(g\left(x\right)\right)}^{-1}=-1\frac{2}{3}x+12\frac{1}{3}$
Question 10:   If $f\left(x\right)=-2x-1$, $g\left(x\right)=-3x+2$ find $f{\left(g\left(4\right)\right)}^{-1}$
$1\frac{2}{3}$
$-\frac{1}{6}$
$2$
$1\frac{1}{2}$