What is the inverse of the function {:[h(x)=(3)/(4)x+12" ? "],[h^(-1)(x)=◻]:}

Concept of finding inverse function: Understand the concept of finding an inverse function. To find the inverse of a function, we need to swap the x and y variables and then solve for y. This process will give us the inverse function, denoted as h^(-1)(x).Writing the original function: Write the original function with y instead of h(x). y = (3/4)x + 12Swapping variables: Swap the x and y variables to begin finding the inverse. x = (3/4)y + 12Solving for y: Solve for y to find the inverse function. First, subtract 12 from both sides of the equation. x - 12 = (3/4)yIsolating y: Multiply both sides of the equation by 4/3 to isolate y. (4/3)(x - 12) = ySimplifying the equation: Simplify the equation to get the inverse function. y = (4/3)x - 16 This is the inverse function, so we can write it as h^(-1)(x) = (4/3)x - 16.

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What is the inverse of the function $h(x)=\frac{3}{4}x+12$ ? $\newline$ $h^{-1}(x)=\square$

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Algebra 2

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Q. What is the inverse of the function

h(x)=\frac{3}{4}x+12

\newline

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

Concept of finding inverse function: Understand the concept of finding an inverse function. To find the inverse of a function, we need to swap the $x$ and $y$ variables and then solve for $y$ . This process will give us the inverse function, denoted as $h^{-1}(x)$ .
Writing the original function: Write the original function with $y$ instead of $h(x)$ . $y = \left(\frac{3}{4}\right)x + 12$
Swapping variables: Swap the $x$ and $y$ variables to begin finding the inverse. $x = \left(\frac{3}{4}\right)y + 12$
Solving for y: Solve for y to find the inverse function. $\newline$ First, subtract $12$ from both sides of the equation. $\newline$ $x - $12$ = \left(\frac{$3$}{$4$}\right)y
Isolating $y$: Multiply both sides of the equation by $\frac{4}{3}$ to isolate $y$.$\left(\frac{4}{3}\right)(x - 12) = y$
Simplifying the equation: Simplify the equation to get the inverse function.$\newline$$y = \frac{4}{3}x - 16$$\newline$This is the inverse function, so we can write it as $h^{-1}(x) = \frac{4}{3}x - 16$.