Find the inverse function in slope-intercept form (mx+b) : f(x)=-(2)/(5)x+8 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 roles of the input and output of the original function. For the function f(x) = y, the inverse function answers the question: for a given y, what x would produce that y?Write Original Function: Write the original function, replacing f(x) with y for convenience. y = -(2/5)x + 8Swap x and y: Swap x and y to find the inverse function. x = -(2/5)y + 8Solve for y: Solve for y to express the inverse function in terms of x. First, isolate the term containing y on one side: (2/5)y = 8 - xMultiply by Reciprocal: Multiply both sides by the reciprocal of the coefficient of y to solve for y. y = (5/2)(8 - x)Distribute (5/2): Distribute the (5/2) across the terms in the parentheses. y = (5/2)*8 - (5/2)*x y = 20 - (5/2)xWrite Final Inverse Function: Write the final inverse function in slope-intercept form. f^(-1)(x) = 20 - (5/2)x

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

f(x)=-(2)/(5)x+8
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=-\frac{2}{5} x+8$ $\newline$ 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+8

\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 roles of the input and output of the original function. For the function $f(x) = y$ , the inverse function answers the question: for a given $y$ , what $x$ would produce that $y$ ?
Write Original Function: Write the original function, replacing $f(x)$ with $y$ for convenience. $y = -\left(\frac{2}{5}\right)x + 8$
Swap x and y: Swap x and y to find the inverse function. $\newline$ $x = -\left(\frac{2}{5}\right)y + 8$
Solve for y: Solve for y to express the inverse function in terms of x. $\newline$ First, isolate the term containing y on one side: $\newline$ $(\frac{2}{5})y = 8 - x$
Multiply by Reciprocal: Multiply both sides by the reciprocal of the coefficient of $y$ to solve for $y$ . $y = \left(\frac{5}{2}\right)(8 - x)$
Distribute $(5/2)$ : Distribute the $(5/2)$ across the terms in the parentheses. $\newline$ $y = (5/2)\cdot8 - (5/2)\cdot x$ $\newline$ $y = 20 - (5/2)x$
Write Final Inverse Function: Write the final inverse function in slope-intercept form. $f^{-1}(x) = 20 - \frac{5}{2}x$