Find the inverse function in slope-intercept form (mx+b) : f(x)=(3)/(2)x+9 Answer: f^(-1)(x)=

Understand Inverse Function: Understand the concept of an inverse function. An inverse function reverses the operation of the original function. If f(x) = y, then f^(-1)(y) = x. To find the inverse function, we need to solve for x in terms of y.Replace with y: Replace f(x) with y to make the equation easier to work with. y = (3/2)x + 9Swap x and y: Swap x and y to find the inverse function. x = (3/2)y + 9Solve for y: Solve for y in terms of x. First, subtract 9 from both sides of the equation. x - 9 = (3/2)yMultiply by reciprocal: Multiply both sides by the reciprocal of (3/2) to solve for y. y = (2/3)(x - 9)Write in slope-intercept form: Write the inverse function in slope-intercept form. f^(-1)(x) = (2/3)x - 6

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

f(x)=(3)/(2)x+9
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=\frac{3}{2} x+9$ $\newline$ 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{3}{2} x+9

\newline

Answer:

f^{-1}(x)=

Understand Inverse Function: Understand the concept of an inverse function. An inverse function reverses the operation of the original function. If $f(x) = y$ , then $f^{-1}(y) = x$ . To find the inverse function, we need to solve for $x$ in terms of $y$ .
Replace with $y$ : Replace $f(x)$ with $y$ to make the equation easier to work with. $y = \left(\frac{3}{2}\right)x + 9$
Swap x and y: Swap x and y to find the inverse function. $\newline$ $x = \frac{3}{2}y + 9$
Solve for y: Solve for y in terms of x. $\newline$ First, subtract $9$ from both sides of the equation. $\newline$ $x - $9$ = \left(\frac{$3$}{$2$}\right)y
Multiply by reciprocal: Multiply both sides by the reciprocal of $(\frac{3}{2})$ to solve for $y$.\[y = \left(\frac{2}{3}\right)(x - 9)\]
Write in slope-intercept form: Write the inverse function in slope-intercept form. $f^{-1}(x) = \frac{2}{3}x - 6$