For the function f(x)=(x^((1)/(3)))/(4), find f^(-1)(x). f^(-1)(x)=4x^((1)/(3)) f^(-1)(x)=4x^(3) f^(-1)(x)=(4x)^(3) f^(-1)(x)=((x)/(4))^(3)

Rewrite function 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 = (x^(1/3))/4Switch x and y: Now, switch x and y to find the inverse function: x = (y^(1/3))/4Isolate y: To solve for y, we need to isolate y on one side of the equation. Start by multiplying both sides by 4 to get rid of the denominator: 4x = y^(1/3)Raise to power of 3: Now, to get rid of the cube root, we raise both sides of the equation to the power of 3: (4x)^3 = (y^(1/3))^3Simplify and find inverse: Simplifying both sides gives us: 64x^3 = yWe have now isolated y and found the inverse function. So, the inverse function is: f^(-1)(x) = 64x^3

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the function
f(x)=(x^((1)/(3)))/(4), find
f^(-1)(x).

f^(-1)(x)=4x^((1)/(3))

f^(-1)(x)=4x^(3)

f^(-1)(x)=(4x)^(3)

f^(-1)(x)=((x)/(4))^(3)

For the function $f(x)=\frac{x^{\frac{1}{3}}}{4}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=4 x^{\frac{1}{3}}$ $\newline$ $f^{-1}(x)=4 x^{3}$ $\newline$ $f^{-1}(x)=(4 x)^{3}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{4}\right)^{3}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. For the function

f(x)=\frac{x^{\frac{1}{3}}}{4}

, find

f^{-1}(x)

\newline

f^{-1}(x)=4 x^{\frac{1}{3}}

\newline

f^{-1}(x)=4 x^{3}

\newline

f^{-1}(x)=(4 x)^{3}

\newline

f^{-1}(x)=\left(\frac{x}{4}\right)^{3}

Rewrite function 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 $f(x)$ : $\newline$ $y = \frac{x^{\frac{1}{3}}}{4}$
Switch x and y: Now, switch x and y to find the inverse function: $x = \frac{y^{\frac{1}{3}}}{4}$
Isolate y: To solve for y, we need to isolate y on one side of the equation. Start by multiplying both sides by $4$ to get rid of the denominator: $\newline$ $4x = y^{\frac{1}{3}}$
Raise to power of $3$ : Now, to get rid of the cube root, we raise both sides of the equation to the power of $3$ : $(4x)^3 = (y^{\frac{1}{3}})^3$
Simplify and find inverse: Simplifying both sides gives us: $64x^3 = y$
Simplify and find inverse: Simplifying both sides gives us: $64x^3 = y$ We have now isolated $y$ and found the inverse function. So, the inverse function is: $f^{-1}(x) = 64x^3$