Find the inverse function of the function f(x)=(5x)^((5)/(9)) on the domain x >= 0. f^(-1)(x)=((x)/(5))^(-(9)/(5)) f^(-1)(x)=((x)/(5))^((9)/(5)) f^(-1)(x)=(x^((9)/(5)))/(5) f^(-1)(x)=(x^(-(9)/(5)))/(5)

Replace with y: To find the inverse function, we start by replacing f(x) with y: y = (5x)^(5/9)Interchange x and y: Next, we interchange x and y to solve for the new y, which will be the inverse function: x = (5y)^(5/9)Raise to power of 9/5: Now, we raise both sides of the equation to the power of 9/5 to eliminate the exponent on the right side: x^(9/5) = 5yDivide by 5: We then divide both sides by 5 to solve for y: y = x^(9/5) / 5Replace with f^(-1)(x): Finally, we replace y with f^(-1)(x) to denote the inverse function: f^(-1)(x) = x^(9/5) / 5

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the inverse function of the function
f(x)=(5x)^((5)/(9)) on the domain
x >= 0.

f^(-1)(x)=((x)/(5))^(-(9)/(5))

f^(-1)(x)=((x)/(5))^((9)/(5))

f^(-1)(x)=(x^((9)/(5)))/(5)

f^(-1)(x)=(x^(-(9)/(5)))/(5)

Find the inverse function of the function $f(x)=(5 x)^{\frac{5}{9}}$ on the domain $x \geq 0$ . $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{9}{5}}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{\frac{9}{5}}$ $\newline$ $f^{-1}(x)=\frac{x^{\frac{9}{5}}}{5}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{9}{5}}}{5}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=(5 x)^{\frac{5}{9}}

on the domain

x \geq 0

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{9}{5}}

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{\frac{9}{5}}

\newline

f^{-1}(x)=\frac{x^{\frac{9}{5}}}{5}

\newline

f^{-1}(x)=\frac{x^{-\frac{9}{5}}}{5}

Replace with $y$ : To find the inverse function, we start by replacing $f(x)$ with $y$ : $y = (5x)^{\frac{5}{9}}$
Interchange $x$ and $y$ : Next, we interchange $x$ and $y$ to solve for the new $y$ , which will be the inverse function: $x = (5y)^{\frac{5}{9}}$
Raise to power of $\frac{9}{5}$ : Now, we raise both sides of the equation to the power of $\frac{9}{5}$ to eliminate the exponent on the right side: $\newline$ $x^{\frac{9}{5}} = 5y$
Divide by $5$ : We then divide both sides by $5$ to solve for $y$ : $y = \frac{x^{(9/5)}}{5}$
Replace with $f^{-1}(x)$ : Finally, we replace $y$ with $f^{-1}(x)$ to denote the inverse function: $\newline$ $f^{-1}(x) = \frac{x^{\frac{9}{5}}}{5}$