Find the inverse function of the function f(x)=root(5)(5x). f^(-1)(x)=(x^(5))/(3125) f^(-1)(x)=(x^(5))/(5) f^(-1)(x)=5x^(5) f^(-1)(x)=3125x^(5)

Write function as y: To find the inverse function, we first write the function as y = root(5)(5x).Express fifth root as power: Next, we express the fifth root as a power: y = (5x)^(1/5).Swap x and y: To find the inverse, we swap x and y, so we have x = (5y)^(1/5).Raise both sides to power of 5: Now we want to solve for y. To do this, we raise both sides of the equation to the power of 5 to eliminate the fifth root: x^5 = (5y)^(1/5 * 5).Simplify right side: Simplifying the right side, we get x^5 = 5y.Isolate y: To isolate y, we divide both sides by 5: y = x^5 / 5.Find inverse function: Now we have the inverse function: f^(-1)(x) = x^5 / 5.

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

f^(-1)(x)=(x^(5))/(3125)

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

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

f^(-1)(x)=3125x^(5)

Find the inverse function of the function $f(x)=\sqrt[5]{5 x}$ . $\newline$ $f^{-1}(x)=\frac{x^{5}}{3125}$ $\newline$ $f^{-1}(x)=\frac{x^{5}}{5}$ $\newline$ $f^{-1}(x)=5 x^{5}$ $\newline$ $f^{-1}(x)=3125 x^{5}$

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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[5]{5 x}

\newline

f^{-1}(x)=\frac{x^{5}}{3125}

\newline

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

\newline

f^{-1}(x)=5 x^{5}

\newline

f^{-1}(x)=3125 x^{5}

Write function as $y$ : To find the inverse function, we first write the function as $y = \sqrt[5]{5x}$ .
Express fifth root as power: Next, we express the fifth root as a power: $y = (5x)^{\frac{1}{5}}$ .
Swap $x$ and $y$ : To find the inverse, we swap $x$ and $y$ , so we have $x = (5y)^{\frac{1}{5}}$ .
Raise both sides to power of $5$ : Now we want to solve for $y$ . To do this, we raise both sides of the equation to the power of $5$ to eliminate the fifth root: $x^5 = (5y)^{\frac{1}{5} \cdot 5}$ .
Simplify right side: Simplifying the right side, we get $x^5 = 5y$ .
Isolate $y$ : To isolate $y$ , we divide both sides by $5$ : $y = \frac{x^5}{5}$ .
Find inverse function: Now we have the inverse function: $f^{-1}(x) = \frac{x^5}{5}.$