For the function f(x)=(3x)/(5x-3), find f^(-1)(x). Answer: f^(-1)(x)=

Rewrite with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by rewriting the function with y instead of f(x): y = (3x)/(5x - 3)Switch x and y: Now, switch x and y to find the inverse: x = (3y)/(5y - 3)Multiply by (5y - 3): Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (5y - 3) to get rid of the fraction: x(5y - 3) = 3yDistribute x: Distribute x on the left side of the equation: 5xy - 3x = 3yMove 3y term: Now, we want to get all terms containing y on one side of the equation and the constant term on the other side. Let's move the 3y term to the left side by subtracting 3y from both sides: 5xy - 3y = 3xFactor out y: Factor out y from the left side of the equation: y(5x - 3) = 3xDivide by (5x - 3): Now, divide both sides by (5x - 3) to solve for y: y = 3x / (5x - 3)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the function
f(x)=(3x)/(5x-3), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{3 x}{5 x-3}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\frac{3 x}{5 x-3}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Rewrite with y: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by rewriting the function with $y$ instead of $f(x)$ : $\newline$ $y = \frac{3x}{5x - 3}$
Switch x and y: Now, switch x and y to find the inverse: $x = \frac{3y}{5y - 3}$
Multiply by $(5y - 3)$ : Next, we need to solve for $y$ . To do this, we'll multiply both sides of the equation by $(5y - 3)$ to get rid of the fraction: $\newline$ $x(5y - 3) = 3y$
Distribute $x$ : Distribute $x$ on the left side of the equation: $5xy - 3x = 3y$
Move $3y$ term: Now, we want to get all terms containing $y$ on one side of the equation and the constant term on the other side. Let's move the $3y$ term to the left side by subtracting $3y$ from both sides: $\newline$ $5xy - 3y = 3x$
Factor out $y$ : Factor out $y$ from the left side of the equation: $\newline$ $y(5x - 3) = 3x$
Divide by $(5x - 3)$ : Now, divide both sides by $(5x - 3)$ to solve for $y$ : $y = \frac{3x}{(5x - 3)}$