Find the inverse function of the function f(x)=4root(5)(x). f^(-1)(x)=(x^(5))/(1024) f^(-1)(x)=(x^(5))/(4) f^(-1)(x)=4x^(5) f^(-1)(x)=1024x^(5)

Understand function and inverse: Understand the function and its inverse. The function f(x) = 4√(5)(x) can be rewritten as f(x) = x^(1/5). To find the inverse function, we need to solve for x in terms of y, where y = f(x).Swap x and y: Swap x and y. To find the inverse, we replace f(x) with y and then swap x and y to get x = y^(1/5).Solve for y: Solve for y. To isolate y, we raise both sides of the equation to the power of 5 to get x^5 = y.Rewrite with f^(-1)(x): Rewrite the equation with f^(-1)(x). Now that we have y on one side, we can rewrite the equation as f^(-1)(x) = x^5.Adjust for coefficient: Adjust for the coefficient in the original function. The original function had a coefficient of 4 in front of the root. To account for this in the inverse function, we need to divide by 4^5, which is 1024. So the inverse function is f^(-1)(x) = (x^5) / 1024.

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Find the inverse function of the function
f(x)=4root(5)(x).

f^(-1)(x)=(x^(5))/(1024)

f^(-1)(x)=(x^(5))/(4)

f^(-1)(x)=4x^(5)

f^(-1)(x)=1024x^(5)

Find the inverse function of the function $f(x)=4 \sqrt[5]{x}$ . $\newline$ $f^{-1}(x)=\frac{x^{5}}{1024}$ $\newline$ $f^{-1}(x)=\frac{x^{5}}{4}$ $\newline$ $f^{-1}(x)=4 x^{5}$ $\newline$ $f^{-1}(x)=1024 x^{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Find the inverse function of the function

f(x)=4 \sqrt[5]{x}

\newline

f^{-1}(x)=\frac{x^{5}}{1024}

\newline

f^{-1}(x)=\frac{x^{5}}{4}

\newline

f^{-1}(x)=4 x^{5}

\newline

f^{-1}(x)=1024 x^{5}

Understand function and inverse: Understand the function and its inverse. $\newline$ The function $f(x) = 4\sqrt{5}(x)$ can be rewritten as $f(x) = x^{1/5}$ . To find the inverse function, we need to solve for $x$ in terms of $y$ , where $y = f(x)$ .
Swap $x$ and $y$ : Swap $x$ and $y$ . $\newline$ To find the inverse, we replace $f(x)$ with $y$ and then swap $x$ and $y$ to get $x = y^{\frac{1}{5}}$ .
Solve for y: Solve for y. $\newline$ To isolate $y$ , we raise both sides of the equation to the power of $5$ to get $x^5 = y$ .
Rewrite with $f^{-1}(x)$ : Rewrite the equation with $f^{-1}(x)$ . $\newline$ Now that we have $y$ on one side, we can rewrite the equation as $f^{-1}(x) = x^5$ .
Adjust for coefficient: Adjust for the coefficient in the original function. $\newline$ The original function had a coefficient of $4$ in front of the root. To account for this in the inverse function, we need to divide by $4^5$ , which is $1024$ . So the inverse function is $f^{-1}(x) = \frac{x^5}{1024}$ .