For the function f(x)=root(7)(((x)/(7))), find f^(-1)(x). f^(-1)(x)=7x^(7) f^(-1)(x)=(x^(7))/(7) f^(-1)(x)=root(7)((7x)) f^(-1)(x)=(7x)^(7)

Understand Function and Goal: Understand the function and the goal. The function f(x) = root(7)((x/7)) is a 7th root function. We need to find its inverse, which means we want to find a function f^(-1)(x) such that f(f^(-1)(x)) = x.Set Equal to y: Set f(x) equal to y for convenience. Let y = f(x) = root(7)((x/7)).Swap x and y: Swap x and y to find the inverse. To find the inverse function, we swap x and y, so we get x = root(7)((y/7)).Solve for y: Solve for y. To isolate y, we need to get rid of the 7th root. We do this by raising both sides of the equation to the 7th power: (x)^7 = (root(7)((y/7)))^7.Simplify Equation: Simplify the equation. When we raise the 7th root to the 7th power, they cancel each other out, so we get: (x)^7 = y/7.Multiply by 7: Multiply both sides by 7 to solve for y. 7 * (x)^7 = 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) = 7x^(7).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the function
f(x)=root(7)(((x)/(7))), find
f^(-1)(x).

f^(-1)(x)=7x^(7)

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

f^(-1)(x)=root(7)((7x))

f^(-1)(x)=(7x)^(7)

For the function $f(x)=\sqrt[7]{\left(\frac{x}{7}\right)}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=7 x^{7}$ $\newline$ $f^{-1}(x)=\frac{x^{7}}{7}$ $\newline$ $f^{-1}(x)=\sqrt[7]{(7 x)}$ $\newline$ $f^{-1}(x)=(7 x)^{7}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\sqrt[7]{\left(\frac{x}{7}\right)}

, find

f^{-1}(x)

\newline

f^{-1}(x)=7 x^{7}

\newline

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

\newline

f^{-1}(x)=\sqrt[7]{(7 x)}

\newline

f^{-1}(x)=(7 x)^{7}

Understand Function and Goal: Understand the function and the goal. $\newline$ The function $f(x) = \sqrt[7]{\left(\frac{x}{7}\right)}$ is a $7^{\text{th}}$ root function. We need to find its inverse, which means we want to find a function $f^{-1}(x)$ such that $f(f^{-1}(x)) = x$ .
Set Equal to y: Set $f(x)$ equal to $y$ for convenience. $\newline$ Let $y = f(x) = \sqrt[7]{\left(\frac{x}{7}\right)}$ .
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse. $\newline$ To find the inverse function, we swap $x$ and $y$ , so we get $x = \sqrt[7]{\left(\frac{y}{7}\right)}$ .
Solve for y: Solve for y. $\newline$ To isolate $y$ , we need to get rid of the $7$ th root. We do this by raising both sides of the equation to the $7$ th power: $\newline$ $(x)^$7$ = (\sqrt[$7$]{(y/$7$)})^$7$.
Simplify Equation: Simplify the equation.$\newline$When we raise the $7$th root to the $7$th power, they cancel each other out, so we get:$\newline$$(x)^7 = \frac{y}{7}$.
Multiply by $7$: Multiply both sides by $7$ to solve for $y$.$7 \times (x)^7 = y$.
Write Inverse Function: Write the inverse function.$\newline$Now that we have $y$ by itself, we can write the inverse function as:$\newline$$f^{-1}(x) = 7x^{7}$.