Find the inverse function in slope-intercept form (mx+b) : f(x)=(5)/(2)x-15 Answer: f^(-1)(x)=

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = (5/2)x - 15. 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 with y: Write the original function with y instead of f(x). Replace f(x) with y to make it easier to find the inverse. y = (5/2)x - 15Swap x and y: Swap x and y to find the inverse. To find the inverse function, we switch x and y. This gives us: x = (5/2)y - 15Solve for y: Solve for y. We need to isolate y on one side of the equation to solve for the inverse function. First, add 15 to both sides of the equation: x + 15 = (5/2)yMultiply by 2/5: Multiply both sides by 2/5 to solve for y. (2/5)(x + 15) = yDistribute and simplify: Distribute 2/5 on the right side of the equation. y = (2/5)x + (2/5)(15)Simplify the equation. y = (2/5)x + 6 This is the inverse function in slope-intercept form.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

f(x)=(5)/(2)x-15
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=\frac{5}{2} x-15$ $\newline$ Answer: $f^{-1}(x)=$

View step-by-step help

Home

Math Problems

Algebra 2

Find the vertex of the transformed function

Full solution

Q. Find the inverse function in slope-intercept form

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

\newline

f(x)=\frac{5}{2} x-15

\newline

Answer:

f^{-1}(x)=

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = \frac{5}{2}x - 15$ . 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 with $y$ : Write the original function with $y$ instead of $f(x)$ . $\newline$ Replace $f(x)$ with $y$ to make it easier to find the inverse. $\newline$ $y = \frac{5}{2}x - 15$
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse. $\newline$ To find the inverse function, we switch $x$ and $y$ . This gives us: $\newline$ $x = \frac{5}{2}y - 15$
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 $15$ to both sides of the equation: $\newline$ $x + $15$ = \left(\frac{$5$}{$2$}\right)y
Multiply by $\frac{2}{5}$: Multiply both sides by $\frac{2}{5}$ to solve for $y$.$\left(\frac{2}{5}\right)(x + 15) = y$
Distribute and simplify: Distribute $\frac{2}{5}$ on the right side of the equation.$y = \left(\frac{2}{5}\right)x + \left(\frac{2}{5}\right)(15)$
Distribute and simplify: Distribute $\frac{2}{5}$ on the right side of the equation.$y = \left(\frac{2}{5}\right)x + \left(\frac{2}{5}\right)(15)$Simplify the equation.$y = \left(\frac{2}{5}\right)x + 6$This is the inverse function in slope-intercept form.