Find the inverse function of the function f(x)=root(3)(5x). f^(-1)(x)=(x^(2))/(25) f^(-1)(x)=(x^(3))/(125) f^(-1)(x)=(x^(3))/(5) f^(-1)(x)=(x^(2))/(5)

Replace with y: To find the inverse function, we start by replacing f(x) with y: y = ∛(5x)Interchange roles to solve: Next, we interchange the roles of x and y to solve for the new y, which will give us the inverse function: x = ∛(5y)Isolate y by cubing: Now, we need to isolate y. To do this, we will cube both sides of the equation to eliminate the cube root: x^3 = (5y)^(3/3) x^3 = 5yDivide by 5: Divide both sides by 5 to solve for y: y = x^3 / 5Write inverse function: Now that we have solved for y, we can write the inverse function. Replace y with f^(-1)(x) to denote the inverse function: f^(-1)(x) = x^3 / 5

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Find the inverse function of the function
f(x)=root(3)(5x).

f^(-1)(x)=(x^(2))/(25)

f^(-1)(x)=(x^(3))/(125)

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

f^(-1)(x)=(x^(2))/(5)

Find the inverse function of the function $f(x)=\sqrt[3]{5 x}$ . $\newline$ $f^{-1}(x)=\frac{x^{2}}{25}$ $\newline$ $f^{-1}(x)=\frac{x^{3}}{125}$ $\newline$ $f^{-1}(x)=\frac{x^{3}}{5}$ $\newline$ $f^{-1}(x)=\frac{x^{2}}{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=\sqrt[3]{5 x}

\newline

f^{-1}(x)=\frac{x^{2}}{25}

\newline

f^{-1}(x)=\frac{x^{3}}{125}

\newline

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

\newline

f^{-1}(x)=\frac{x^{2}}{5}

Replace with $y$ : To find the inverse function, we start by replacing $f(x)$ with $y$ : $y = \sqrt[3]{5x}$
Interchange roles to solve: Next, we interchange the roles of $x$ and $y$ to solve for the new $y$ , which will give us the inverse function: $\newline$ $x = \sqrt[3]{5y}$
Isolate y by cubing: Now, we need to isolate y. To do this, we will cube both sides of the equation to eliminate the cube root: $\newline$ $x^3 = (5y)^{\frac{3}{3}}$ $\newline$ $x^3 = 5y$
Divide by $5$ : Divide both sides by $5$ to solve for $y$ : $y = \frac{x^3}{5}$
Write inverse function: Now that we have solved for $y$ , we can write the inverse function. Replace $y$ with $f^{-1}(x)$ to denote the inverse function: $\newline$ $f^{-1}(x) = \frac{x^3}{5}$