Find the inverse function of the function f(x)=(3x)^(-(5)/(3)) on the domain x > 0. f^(-1)(x)=((x)/(3))^((3)/(5)) f^(-1)(x)=(x^((3)/(5)))/(3) f^(-1)(x)=((x)/(3))^(-(3)/(5)) f^(-1)(x)=(x^(-(3)/(5)))/(3)

Write function as y: To find the inverse function, we first write the function as y = (3x)^(-(5)/(3)).Swap x and y: Next, we swap x and y to find the inverse function. This gives us x = (3y)^(-(5)/(3)).Raise both sides: Now, we solve for y. To do this, we raise both sides of the equation to the power of (-3/5) to get rid of the negative exponent on the right side. This gives us x^(-(3)/(5)) = 3y.Divide to isolate y: Next, we divide both sides of the equation by 3 to isolate y. This gives us y = (x^(-(3)/(5)))/3.Take reciprocal of exponent: We can also write the inverse function in an equivalent form by taking the reciprocal of the exponent. This gives us y = ((x)/(3))^((3)/(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)=(3x)^(-(5)/(3)) on the domain
x > 0.

f^(-1)(x)=((x)/(3))^((3)/(5))

f^(-1)(x)=(x^((3)/(5)))/(3)

f^(-1)(x)=((x)/(3))^(-(3)/(5))

f^(-1)(x)=(x^(-(3)/(5)))/(3)

Find the inverse function of the function $f(x)=(3 x)^{-\frac{5}{3}}$ on the domain x>0 . $\newline$ $f^{-1}(x)=\left(\frac{x}{3}\right)^{\frac{3}{5}}$ $\newline$ $f^{-1}(x)=\frac{x^{\frac{3}{5}}}{3}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{3}\right)^{-\frac{3}{5}}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{3}{5}}}{3}$

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

on the domain

x>0

\newline

f^{-1}(x)=\left(\frac{x}{3}\right)^{\frac{3}{5}}

\newline

f^{-1}(x)=\frac{x^{\frac{3}{5}}}{3}

\newline

f^{-1}(x)=\left(\frac{x}{3}\right)^{-\frac{3}{5}}

\newline

f^{-1}(x)=\frac{x^{-\frac{3}{5}}}{3}

Write function as $y$ : To find the inverse function, we first write the function as $y = (3x)^{-\frac{5}{3}}$ .
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function. This gives us $x = (3y)^{-(\frac{5}{3})}$ .
Raise both sides: Now, we solve for $y$ . To do this, we raise both sides of the equation to the power of $(-\frac{3}{5})$ to get rid of the negative exponent on the right side. This gives us $x^{-(\frac{3}{5})} = 3y$ .
Divide to isolate $y$ : Next, we divide both sides of the equation by $3$ to isolate $y$ . This gives us $y = \frac{x^{-(\frac{3}{5})}}{3}$ .
Take reciprocal of exponent: We can also write the inverse function in an equivalent form by taking the reciprocal of the exponent. This gives us $y = \left(\frac{x}{3}\right)^{\frac{3}{5}}$ .