Targeted Review Solutions

1. $f\left(x\right)=\frac{3}{x–2}$

$$\begin{gathered} y=\frac{3}{x–2} \\ x=\frac{3}{y–2} \\ x\left(y–2\right)=3 \\ y–2=\frac{3}{x} \\ y=\frac{3}{x}+2 \end{gathered}$$

$f^{–1}\left(x\right)=\frac{3}{x}+2$

2. $g\left(x\right)=\sqrt{x+3}$

$$\begin{gathered} y=\sqrt{x+3} \\ {\left(x\right)}^2={\left(\sqrt{y+3}\right)}^{2 } \\ x^2=y+3 \\ y=x^2–3 \end{gathered}$$

$g^{–1}\left(x\right)=x^2–3$

3. $2^{x+9}$

$$\begin{gathered} 2^{\left(–5\right)+9} \\ {2}^4 \end{gathered}$$

16

4. $x^{8+x }$

$$\begin{gathered} {\left(–5\right)}^{8+\left(–5\right)} \\ {\left(–5\right)}^3 \end{gathered}$$

–125

5. $5^x\left(5^{3–x}\right)$

$$\begin{gathered} 5^{–3}\left(5^{3–\left(–3\right)}\right) \\ \frac{1}{5^3}\left(5^0\right) \\ \frac{1}{125}\left(1\right) \end{gathered}$$

$\frac{1}{125}$

6. ${\left(\frac{2}{3}\right)}^x{x}^{x }$

$$\begin{gathered} {\left(\frac{2}{3}\right)}^{–3}{\left(–3\right)}^{–3} \\ \frac{{\left(2\right)}^{–3}}{{\left(3\right)}^{–3}}·\frac{1}{{\left(–3\right)}^3} \\ \frac{{\left(3\right)}^3}{{\left(2\right)}^3}·\frac{1}{{\left(–3\right)}^3} \\ \frac{27}{8}·\frac{1}{–27} \end{gathered}$$

$–\frac{1}{8}$

7. A square root function translated 2 units right and one unit up from the parent function

$$\begin{gathered} a=1, h=2, k=1 \\ y=a\sqrt{x–h}+k \end{gathered}$$

$y=\sqrt{x–2}+1$

8. A quadratic function reflected across the x-axis, translated up 5 units and left 8 units

$$\begin{gathered} a=–1, h=–8, k=5 \\ y=a{\left(x–h\right)}^2+k \end{gathered}$$

$y=–{\left(x+8\right)}^2+5$