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

Understand Inverse Function: Understand the concept of an inverse function. An inverse function, denoted as h^(-1)(x), is a function that reverses the effect of the original function h(x). For a function h(x), the inverse h^(-1)(x) will satisfy the condition that h(h^(-1)(x)) = x and h^(-1)(h(x)) = x.Write Original Function: Write down the original function. The original function is given as h(x) = (3/2)(x - 11).Replace with y: Replace h(x) with y to make the equation easier to work with. y = (3/2)(x - 11)Swap x and y: Swap x and y to find the inverse function. x = (3/2)(y - 11)Solve for y: Solve for y to find the inverse function. Multiply both sides by 2/3 to isolate the term with y: (2/3)x = y - 11Add 11 to Solve: Add 11 to both sides to solve for y. y = (2/3)x + 11Replace with Inverse: Replace y with h^(-1)(x) to denote the inverse function. h^(-1)(x) = (2/3)x + 11

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

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Q. What is the inverse of the function

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

\newline

h^{-1}(x)=\square

Understand Inverse Function: Understand the concept of an inverse function. An inverse function, denoted as $h^{-1}(x)$ , is a function that reverses the effect of the original function $h(x)$ . For a function $h(x)$ , the inverse $h^{-1}(x)$ will satisfy the condition that $h(h^{-1}(x)) = x$ and $h^{-1}(h(x)) = x$ .
Write Original Function: Write down the original function. $\newline$ The original function is given as $h(x) = \left(\frac{3}{2}\right)(x - 11)$ .
Replace with $y$ : Replace $h(x)$ with $y$ to make the equation easier to work with. $\newline$ $y = \left(\frac{3}{2}\right)(x - 11)$
Swap x and y: Swap x and y to find the inverse function. $\newline$ $x = \frac{3}{2}(y - 11)$
Solve for $y$ : Solve for $y$ to find the inverse function. $\newline$ Multiply both sides by $\frac{2}{3}$ to isolate the term with $y$ : $\newline$ $\left(\frac{2}{3}\right)x = y - 11$
Add $11$ to Solve: Add $11$ to both sides to solve for $y$ . $\newline$ $y = \left(\frac{2}{3}\right)x + 11$
Replace with Inverse: Replace $y$ with $h^{-1}(x)$ to denote the inverse function. $h^{-1}(x) = \frac{2}{3}x + 11$