[tex]\begin{gathered} \text{Answer} \\ f^{-1}(x)\text{ = }\frac{3x\text{ - 15}}{4} \end{gathered}[/tex]
Explanation:
[tex]\begin{gathered} \text{Given that} \\ f(x)\text{ = }\frac{4}{3}x\text{ + 5} \\ \text{ Find f(x)}^{-1} \\ \text{Step 1: Rewrite f(x) as y} \\ y\text{ = }\frac{4}{3}x\text{ + }5 \\ \text{Step 2: Swap x and y} \\ x\text{ = }\frac{4}{3}y\text{ + 5} \\ 3x\text{ = 4y + 15} \\ \text{Solve for y} \\ 3x\text{ - 15 = 4y} \\ 4y\text{ = 3x - 15} \\ \text{Divide both sides by 4} \\ y\text{ = }\frac{3}{4}x\text{ - }\frac{15}{4} \\ y\text{ = }\frac{3x\text{ - 15}}{4} \\ Sincey=f^{-1}(x)^{} \\ \text{ f}^{-1}(x)\text{ = }\frac{3x\text{ - 15}}{4} \end{gathered}[/tex]
