Find the inverse function in slope-intercept form (mx+b) : f(x)=-(5)/(2)x-10 Answer: f^(-1)(x)=

Understand Inverse Function Concept: Understand the concept of an inverse function. An inverse function, denoted as f^(-1)(x), swaps the x and y values of the original function. For the function f(x) = y, the inverse function would satisfy the equation x = f^(-1)(y). To find the inverse function in slope-intercept form, we need to solve for y in terms of x.Write Original Function: Write the original function, replacing f(x) with y. y = -(5/2)x - 10 This is the starting point for finding the inverse function.Swap x and y: Swap x and y to begin finding the inverse function. x = -(5/2)y - 10 By swapping x and y, we are setting up the equation to solve for the inverse function.Solve for Inverse Function: Solve for y to find the inverse function. First, add 10 to both sides of the equation to isolate the term with y on one side: x + 10 = -(5/2)y Next, multiply both sides by -2/5 to solve for y: y = (-2/5)(x + 10)Simplify Inverse Function: Simplify the expression for the inverse function. y = (-2/5)x - 4 This is the inverse function in slope-intercept form, where the slope is -2/5 and the y-intercept is -4.

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

f(x)=-(5)/(2)x-10
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=-\frac{5}{2} x-10$ $\newline$ 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{5}{2} x-10

\newline

Answer:

f^{-1}(x)=

Understand Inverse Function Concept: Understand the concept of an inverse function. An inverse function, denoted as $f^{-1}(x)$ , swaps the $x$ and $y$ values of the original function. For the function $f(x) = y$ , the inverse function would satisfy the equation $x = f^{-1}(y)$ . To find the inverse function in slope-intercept form, we need to solve for $y$ in terms of $x$ .
Write Original Function: Write the original function, replacing $f(x)$ with $y$ . $y = -\left(\frac{5}{2}\right)x - 10$ This is the starting point for finding the inverse function.
Swap $x$ and $y$ : Swap $x$ and $y$ to begin finding the inverse function. $\newline$ $x = -\left(\frac{5}{2}\right)y - 10$ $\newline$ By swapping $x$ and $y$ , we are setting up the equation to solve for the inverse function.
Solve for Inverse Function: Solve for $y$ to find the inverse function. $\newline$ First, add $10$ to both sides of the equation to isolate the term with $y$ on one side: $\newline$ $x + 10 = -(\frac{5}{2})y$ $\newline$ Next, multiply both sides by $-\frac{2}{5}$ to solve for $y$ : $\newline$ $y = (-\frac{2}{5})(x + 10)$
Simplify Inverse Function: Simplify the expression for the inverse function. $\newline$ $y = \frac{-2}{5}x - 4$ $\newline$ This is the inverse function in slope-intercept form, where the slope is $\frac{-2}{5}$ and the y-intercept is $-4$ .