Find the inverse function in slope-intercept form (mx+b) : f(x)=-(2)/(3)x+12 Answer: f^(-1)(x)=

Replace with y: To find the inverse function, we first replace f(x) with y to make the equation easier to work with. y = -(2/3)x + 12Swap x and y: Next, we swap x and y to find the inverse function. This means we replace y with x and x with y in the equation. x = -(2/3)y + 12Solve for y: Now, we need to solve for y to get the inverse function in slope-intercept form (y = mx + b). First, we'll move the term involving y to one side of the equation and the constant to the other side. (2/3)y = -x + 12Isolate y: To isolate y, we multiply both sides of the equation by the reciprocal of (2/3), which is (3/2). y = (3/2)(-x + 12)Distribute and simplify: We distribute (3/2) across the terms inside the parentheses. y = (3/2)(-x) + (3/2)(12)Final inverse function: Now we simplify the equation by multiplying the constants. y = -3/2 x + 18We have found the inverse function in slope-intercept form. The inverse function of f(x) = -(2/3)x + 12 is: f^(-1)(x) = -3/2 x + 18

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)=-(2)/(3)x+12
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=-\frac{2}{3} x+12$ $\newline$ 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{2}{3} x+12

\newline

Answer:

f^{-1}(x)=

Replace with $y$ : To find the inverse function, we first replace $f(x)$ with $y$ to make the equation easier to work with. $\newline$ $y = -\left(\frac{2}{3}\right)x + 12$
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function. This means we replace $y$ with $x$ and $x$ with $y$ in the equation. $\newline$ $x = -\left(\frac{2}{3}\right)y + 12$
Solve for y: Now, we need to solve for y to get the inverse function in slope-intercept form $y = mx + b$ . First, we'll move the term involving $y$ to one side of the equation and the constant to the other side. $\frac{2}{3}y = -x + 12$
Isolate y: To isolate y, we multiply both sides of the equation by the reciprocal of $(\frac{2}{3})$ , which is $(\frac{3}{2})$ . $\newline$ $y = (\frac{3}{2})(-x + 12)$
Distribute and simplify: We distribute $(\frac{3}{2})$ across the terms inside the parentheses. $\newline$ $y = (\frac{3}{2})(-x) + (\frac{3}{2})(12)$
Final inverse function: Now we simplify the equation by multiplying the constants. $y = -\frac{3}{2} x + 18$
Final inverse function: Now we simplify the equation by multiplying the constants. $\newline$ $y = -\frac{3}{2} x + 18$ We have found the inverse function in slope-intercept form. The inverse function of $f(x) = -\left(\frac{2}{3}\right)x + 12$ is: $\newline$ $f^{-1}(x) = -\frac{3}{2} x + 18$