Find the inverse function of the function f(x)=4x^((9)/(7)) on the domain x >= 0. f^(-1)(x)=((x)/(4))^(-(7)/(9)) f^(-1)(x)=((x)/(4))^((7)/(9)) f^(-1)(x)=(x^(-(7)/(9)))/(4) f^(-1)(x)=(x^((7)/(9)))/(4)

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = 4x^(9/7). The inverse function, denoted as f^(-1)(x), will undo the operation performed by f(x). To find the inverse, we will switch the roles of x and y and solve for y.Write original function: Write the original function with y instead of f(x). Let y = 4x^(9/7). This is the first step in finding the inverse function.Swap x and y: Swap x and y to find the inverse. Now, we replace y with x and x with y to get x = 4y^(9/7).Solve for y: Solve for y. To isolate y, we need to get rid of the coefficient 4 and the exponent (9/7). We start by dividing both sides by 4, which gives us x/4 = y^(9/7).Take to power: Take both sides to the power of (7/9) to cancel the exponent on y. Raise both sides of the equation to the power of (7/9) to get (x/4)^(7/9) = y.Write inverse function: Write the inverse function. Now that we have y by itself, we can write the inverse function as f^(-1)(x) = (x/4)^(7/9).

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)=4x^((9)/(7)) on the domain
x >= 0.

f^(-1)(x)=((x)/(4))^(-(7)/(9))

f^(-1)(x)=((x)/(4))^((7)/(9))

f^(-1)(x)=(x^(-(7)/(9)))/(4)

f^(-1)(x)=(x^((7)/(9)))/(4)

Find the inverse function of the function $f(x)=4 x^{\frac{9}{7}}$ on the domain $x \geq 0$ . $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{7}{9}}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{7}{9}}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{7}{9}}}{4}$ $\newline$ $f^{-1}(x)=\frac{x^{\frac{7}{9}}}{4}$

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)=4 x^{\frac{9}{7}}

on the domain

x \geq 0

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{-\frac{7}{9}}

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{\frac{7}{9}}

\newline

f^{-1}(x)=\frac{x^{-\frac{7}{9}}}{4}

\newline

f^{-1}(x)=\frac{x^{\frac{7}{9}}}{4}

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = 4x^{(9/7)}$ . The inverse function, denoted as $f^{-1}(x)$ , will undo the operation performed by $f(x)$ . To find the inverse, we will switch the roles of $x$ and $y$ and solve for $y$ .
Write original function: Write the original function with $y$ instead of $f(x)$ . $\newline$ Let $y = 4x^{(9/7)}$ . This is the first step in finding the inverse function.
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse. $\newline$ Now, we replace $y$ with $x$ and $x$ with $y$ to get $x = 4y^{(9/7)}$ .
Solve for y: Solve for y. $\newline$ To isolate $y$ , we need to get rid of the coefficient $4$ and the exponent $(9/7)$ . We start by dividing both sides by $4$ , which gives us $x/4 = y^{(9/7)}$ .
Take to power: Take both sides to the power of $(7/9)$ to cancel the exponent on $y$ . Raise both sides of the equation to the power of $(7/9)$ to get $(x/4)^{(7/9)} = y$ .
Write inverse function: Write the inverse function. $\newline$ Now that we have $y$ by itself, we can write the inverse function as $f^{-1}(x) = \left(\frac{x}{4}\right)^{\frac{7}{9}}$ .