Find the inverse function in slope-intercept form (mx+b) : f(x)=(2)/(3)x-12 Answer: f^(-1)(x)=

Write Function: Write down the original function. The original function is f(x) = (2/3)x - 12.Replace with y: Replace f(x) with y to make the equation easier to work with. y = (2/3)x - 12Swap x and y: To find the inverse function, we need to solve for x in terms of y. First, swap x and y in the equation. x = (2/3)y - 12Isolate y: Solve for y by isolating it on one side of the equation. Start by adding 12 to both sides. x + 12 = (2/3)yMultiply by Reciprocal: Multiply both sides by the reciprocal of (2/3) to solve for y. y = (3/2)(x + 12)Distribute Terms: Distribute (3/2) to both terms inside the parentheses. y = (3/2)x + (3/2)*12Simplify Constant: Simplify the constant term (3/2)*12. y = (3/2)x + 18Replace with Inverse: Replace y with f^(-1)(x) to denote the inverse function. f^(-1)(x) = (3/2)x + 18

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Find the inverse function in slope-intercept form
(mx+b) :

f(x)=(2)/(3)x-12
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=\frac{2}{3} x-12$ $\newline$ Answer: $f^{-1}(x)=$

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Algebra 2

Find the vertex of the transformed function

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Q. Find the inverse function in slope-intercept form

(\mathrm{mx}+\mathrm{b})

\newline

f(x)=\frac{2}{3} x-12

\newline

Answer:

f^{-1}(x)=

Write Function: Write down the original function. $\newline$ The original function is $f(x) = \frac{2}{3}x - 12$ .
Replace with $y$ : Replace $f(x)$ with $y$ to make the equation easier to work with. $\newline$ $y = \frac{2}{3}x - 12$
Swap x and y: To find the inverse function, we need to solve for $x$ in terms of $y$ . First, swap $x$ and $y$ in the equation. $\newline$ $x = \left(\frac{2}{3}\right)y - 12$
Isolate y: Solve for y by isolating it on one side of the equation. Start by adding $12$ to both sides. $\newline$ $x + 12 = \left(\frac{2}{3}\right)y$
Multiply by Reciprocal: Multiply both sides by the reciprocal of $(\frac{2}{3})$ to solve for $y$ . $y = \left(\frac{3}{2}\right)(x + 12)$
Distribute Terms: Distribute $(\frac{3}{2})$ to both terms inside the parentheses. $\newline$ $y = (\frac{3}{2})x + (\frac{3}{2})\cdot 12$
Simplify Constant: Simplify the constant term $(\frac{3}{2})\cdot 12$ . $y = (\frac{3}{2})x + 18$
Replace with Inverse: Replace $y$ with $f^{-1}(x)$ to denote the inverse function. $f^{-1}(x) = \frac{3}{2}x + 18$