Find the inverse function in slope-intercept form (mx+b) : f(x)=(3)/(2)x+6 Answer: f^(-1)(x)=

Understand Inverse Function: 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 f(x). For the inverse to exist, f(x) must be a one-to-one function, meaning that for every x there is a unique y, and for every y there is a unique x.Write Original Function: Write down the original function. The original function is f(x) = (3/2)x + 6.Replace with y: Replace f(x) with y to make the equation easier to work with. y = (3/2)x + 6Swap x and y: Swap x and y to find the inverse function. x = (3/2)y + 6Solve for Inverse: Solve for y to get the inverse function. Subtract 6 from both sides of the equation: x - 6 = (3/2)y Multiply both sides by 2/3 to isolate y: (2/3)(x - 6) = y y = (2/3)x - 4Replace with f^(-1)(x): Replace y with f^(-1)(x) to denote the inverse function. f^(-1)(x) = (2/3)x - 4

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)=(3)/(2)x+6
Answer:
f^(-1)(x)=

Find the inverse function in slope-intercept form $(\mathrm{mx}+\mathrm{b})$ : $\newline$ $f(x)=\frac{3}{2} x+6$ $\newline$ 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{3}{2} x+6

\newline

Answer:

f^{-1}(x)=

Understand Inverse Function: 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 $f(x)$ . For the inverse to exist, $f(x)$ must be a one-to-one function, meaning that for every $x$ there is a unique $y$ , and for every $y$ there is a unique $x$ .
Write Original Function: Write down the original function. $\newline$ The original function is $f(x) = \frac{3}{2}x + 6$ .
Replace with $y$ : Replace $f(x)$ with $y$ to make the equation easier to work with. $y = \left(\frac{3}{2}\right)x + 6$
Swap x and y: Swap x and y to find the inverse function. $\newline$ $x = \frac{3}{2}y + 6$
Solve for Inverse: Solve for $y$ to get the inverse function. $\newline$ Subtract $6$ from both sides of the equation: $\newline$ $x - 6 = \left(\frac{3}{2}\right)y$ $\newline$ Multiply both sides by $\frac{2}{3}$ to isolate $y$ : $\newline$ $\left(\frac{2}{3}\right)(x - 6) = y$ $\newline$ $y = \left(\frac{2}{3}\right)x - 4$
Replace with $f^{-1}(x)$ : Replace $y$ with $f^{-1}(x)$ to denote the inverse function. $\newline$ $f^{-1}(x) = \frac{2}{3}x - 4$