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$What is the inverse of the function {:[h(x)=(3)/(2)(x-11)?],[h^(-1)(x)=]:}$

What is the inverse of the function $h(x) = \frac{3}{2}(x - 11)$ ? $h^{-1}(x) =$

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Identify inverse functions

Full solution

Q. What is the inverse of the function

h(x) = \frac{3}{2}(x - 11)

?

h^{-1}(x) =

Rewriting the function: To find the inverse of the function $h(x)$ , we need to switch the roles of $x$ and $y$ and then solve for $y$ . Let's start by rewriting the function with $y$ instead of $h(x)$ : $\newline$ $y = \left(\frac{3}{2}\right)(x - 11)$
Switching x and y: Now, we switch x and y to find the inverse: $\newline$ $x = \left(\frac{3}{2}\right)(y - 11)$
Solving for y: Next, we solve for y. Start by multiplying both sides by $\frac{2}{3}$ to isolate the term with y: $\newline$ $\left(\frac{2}{3}\right)x = y - 11$
Adding $11$ : Now, add $11$ to both sides to solve for $y$ : $y = \left(\frac{2}{3}\right)x + 11$
Inverse function: We have found the expression for $y$ in terms of $x$ , which is the inverse function of $h(x)$ . Therefore, the inverse function $h^{-1}(x)$ is: $\newline$ $h^{-1}(x) = \left(\frac{2}{3}\right)x + 11$

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