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

Write function as y: To find the inverse function, we first write the function as y = root(3)((4x)).Express cube root as exponent: Next, we express the cube root as an exponent: y = (4x)^(1/3).Swap x and y: To find the inverse, we swap x and y, so we get x = (4y)^(1/3).Cube both sides: Now we need to solve for y. To do this, we cube both sides of the equation to get rid of the cube root: x^3 = 4y.Isolate y: Divide both sides by 4 to isolate y: y = (x^3)/4.Find inverse function: Now we have the inverse function, which we denote as f^(-1)(x): f^(-1)(x) = (x^3)/4.

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

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

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

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

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

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

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Math Problems

Algebra 2

Simplify the product of two radical expressions having same variable

Full solution

Q. For the function

f(x)=\sqrt[3]{(4 x)}

, find

f^{-1}(x)

\newline

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

\newline

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

\newline

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

\newline

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

Write function as $y$ : To find the inverse function, we first write the function as $y = \sqrt[3]{4x}$ .
Express cube root as exponent: Next, we express the cube root as an exponent: $y = (4x)^{\frac{1}{3}}$ .
Swap $x$ and $y$ : To find the inverse, we swap $x$ and $y$ , so we get $x = (4y)^{\frac{1}{3}}$ .
Cube both sides: Now we need to solve for $y$ . To do this, we cube both sides of the equation to get rid of the cube root: $x^3 = 4y$ .
Isolate $y$ : Divide both sides by $4$ to isolate $y$ : $y = \frac{x^3}{4}$ .
Find inverse function: Now we have the inverse function, which we denote as $f^{-1}(x)$ : $f^{-1}(x) = \frac{x^3}{4}$ .