Question

Can you please help me understand how to do this

Answer 1

`\begin{gathered} \text{Answer} \\ f^(-1)(x)\text{ = }\frac{3x\text{ - 15}}{4} \end{gathered}`

Step-by-step explanation:

`\begin{gathered} \text{Given that} \\ f(x)\text{ = }(4)/(3)x\text{ + 5} \\ \text{ Find f(x)}^(-1) \\ \text{Step 1: Rewrite f(x) as y} \\ y\text{ = }(4)/(3)x\text{ + }5 \\ \text{Step 2: Swap x and y} \\ x\text{ = }(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{ = }(3)/(4)x\text{ - }(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}`