Question

What’s the answer for this problem? It’s okay if you can just show me what’s the inverse for this equation

Answer 1

Answer: $Inverse\text{ of function y = }\frac{(x\text{ +}1)^2}{9}-2$

Explanation:

Given:

$\text{y = 3}\sqrt{x+2}\text{ - 1}$

To find:

the inverse of the function

To determine the inverse of the function, first we will interchange x and y:

$x\text{ = 3}\sqrt{y\text{ + 2}}\text{ - 1}$

Next is to solve for y by making it the subject of formula

$\begin{gathered} x\text{ = 3}\sqrt{y\text{ +2}}\text{ -1} \\ Add\text{ 1 to both sides:} \\ \text{x + 1 = 3}\sqrt{y\text{ + 2}} \\ \\ divide\text{ both sies by 3:} \\ \frac{x\text{ + 1}}{3}=\text{ }\frac{\text{3}\sqrt{y\text{ + 2}}}{3} \\ \frac{x\text{ + 1}}{3}=\text{ }\sqrt{y\text{ + 2}} \end{gathered}$$\begin{gathered} square\text{ both sides:} \\ (\frac{x\text{ + 1}}{3})^2\text{ = \lparen}\sqrt{y+2})^2 \\ (\frac{x\text{ + 1}}{3})^2\text{ = y + 2} \\ \\ subtract\text{ 2 from both sides:} \\ (\frac{x\text{ + 1}}{3})^2\text{ - 2 = y } \\ y\text{ = \lparen}\frac{x\text{ + 1}}{3})^2\text{ - 2 = }\frac{(x\text{ + 1\rparen}^2}{3^2}\text{ - 2} \\ \\ y\text{ = }\frac{(x\text{ + 1\rparen}^2}{9}-2 \end{gathered}$$Inverse\text{ of function y = }\frac{(x\text{ +}1)^2}{9}-2$