Find the inverse function in slope-intercept form (mx+b) : f(x)=-(2)/(5)x-16 Answer: f^(-1)(x)=

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = -(2/5)x - 16. The inverse function, denoted as f^(-1)(x), will undo the operation of f(x). To find the inverse, we will switch the roles of x and y and then solve for y.Write the function: Write the function f(x) as an equation with y. Replace f(x) with y to get the equation in terms of x and y. y = -(2/5)x - 16Swap x and y: Swap x and y to find the inverse. To find the inverse function, we switch x and y in the equation. x = -(2/5)y - 16Solve for y: Solve for y. We need to isolate y on one side of the equation to solve for the inverse function. First, add 16 to both sides of the equation: x + 16 = -(2/5)yMultiply both sides: Multiply both sides by -5/2 to solve for y. To isolate y, we multiply both sides by the reciprocal of -2/5, which is -5/2. (-5/2)(x + 16) = yDistribute -5/2: Distribute -5/2 on the left side of the equation. Now we distribute -5/2 to both x and 16. y = (-5/2)x - (5/2)*16Simplify the equation: Simplify the equation. We need to multiply -5/2 by 16 to simplify the equation. y = (-5/2)x - (5/2)*16 y = (-5/2)x - 40Write the inverse function: Write the inverse function in slope-intercept form. The inverse function in slope-intercept form is: f^(-1)(x) = (-5/2)x - 40

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

f(x)=-(2)/(5)x-16
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=-\frac{2}{5} x-16$ $\newline$ 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}{5} x-16

\newline

Answer:

f^{-1}(x)=

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = -\frac{2}{5}x - 16$ . The inverse function, denoted as $f^{-1}(x)$ , will undo the operation of $f(x)$ . To find the inverse, we will switch the roles of $x$ and $y$ and then solve for $y$ .
Write the function: Write the function $f(x)$ as an equation with $y$ . Replace $f(x)$ with $y$ to get the equation in terms of $x$ and $y$ . $y = -\left(\frac{2}{5}\right)x - 16$
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse. $\newline$ To find the inverse function, we switch $x$ and $y$ in the equation. $\newline$ $x = -\left(\frac{2}{5}\right)y - 16$
Solve for y: Solve for y. $\newline$ We need to isolate $y$ on one side of the equation to solve for the inverse function. $\newline$ First, add $16$ to both sides of the equation: $\newline$ $x + $16$ = -\left(\frac{$2$}{$5$}\right)y
Multiply both sides: Multiply both sides by $-\frac{5}{2}$ to solve for $y$. To isolate $y$, we multiply both sides by the reciprocal of $-\frac{2}{5}$, which is $-\frac{5}{2}$. $\left(-\frac{5}{2}\right)(x + 16) = y$
Distribute $-\frac{5}{2}$: Distribute $-\frac{5}{2}$ on the left side of the equation.$\newline$Now we distribute $-\frac{5}{2}$ to both $x$ and $16$.$\newline$$y = \left(-\frac{5}{2}\right)x - \left(\frac{5}{2}\right)\cdot16$
Simplify the equation: Simplify the equation.$\newline$We need to multiply $-\frac{5}{2}$ by $16$ to simplify the equation.$\newline$$y = \left(-\frac{5}{2}\right)x - \left(\frac{5}{2}\right)\cdot16$$\newline$$y = \left(-\frac{5}{2}\right)x - 40$
Write the inverse function: Write the inverse function in slope-intercept form.$\newline$The inverse function in slope-intercept form is:$\newline$$f^{-1}(x) = \frac{-5}{2}x - 40$