Find the inverse function of the function f(x)=2root(5)(x). f^(-1)(x)=-(x^(5))/(32) f^(-1)(x)=(x^(5))/(32) f^(-1)(x)=-(x^(5))/(2) f^(-1)(x)=(x^(5))/(2)

Understand function form: Understand the function and its form. The given function is f(x) = 2√(5)(x), which means f(x) = 2 * x^(1/5). To find the inverse function, we need to solve for x in terms of y, where y = f(x).Replace with y: Replace f(x) with y to prepare for finding the inverse. Let y = 2 * x^(1/5).Solve for x: Solve for x in terms of y. To isolate x, we first divide both sides by 2. y / 2 = x^(1/5)Raise to power 5: Raise both sides to the power of 5 to eliminate the fifth root. (y / 2)^5 = (x^(1/5))^5Replace with f^(-1)(x): Simplify both sides. (y / 2)^5 = xExpand expression: Replace y with f^(-1)(x) to express the inverse function. f^(-1)(x) = (x / 2)^5Calculate 2^5: Expand the expression. f^(-1)(x) = (x^5) / (2^5)Write final expression: Calculate 2^5. 2^5 = 32Write the final expression for the inverse function. f^(-1)(x) = (x^5) / 32

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Find the inverse function of the function
f(x)=2root(5)(x).

f^(-1)(x)=-(x^(5))/(32)

f^(-1)(x)=(x^(5))/(32)

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

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

Find the inverse function of the function $f(x)=2 \sqrt[5]{x}$ . $\newline$ $f^{-1}(x)=-\frac{x^{5}}{32}$ $\newline$ $f^{-1}(x)=\frac{x^{5}}{32}$ $\newline$ $f^{-1}(x)=-\frac{x^{5}}{2}$ $\newline$ $f^{-1}(x)=\frac{x^{5}}{2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=2 \sqrt[5]{x}

\newline

f^{-1}(x)=-\frac{x^{5}}{32}

\newline

f^{-1}(x)=\frac{x^{5}}{32}

\newline

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

\newline

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

Understand function form: Understand the function and its form. $\newline$ The given function is $f(x) = 2\sqrt{5}(x)$ , which means $f(x) = 2 \times x^{1/5}$ . To find the inverse function, we need to solve for $x$ in terms of $y$ , where $y = f(x)$ .
Replace with $y$ : Replace $f(x)$ with $y$ to prepare for finding the inverse. $\newline$ Let $y = 2 \cdot x^{\frac{1}{5}}$ .
Solve for x: Solve for x in terms of y. $\newline$ To isolate x, we first divide both sides by $2$ . $\newline$ $\frac{y}{2} = x^{\frac{1}{5}}$
Raise to power $5$ : Raise both sides to the power of $5$ to eliminate the fifth root. $\newline$ $\left(\frac{y}{$2$}\right)^$5$ = \left(x^{\frac{$1$}{$5$}}\right)^$5$
Replace with $f^{-1}(x)$: Simplify both sides.$\left(\frac{y}{2}\right)^5 = x$
Expand expression: Replace $y$ with $f^{-1}(x)$ to express the inverse function.$\newline$$f^{-1}(x) = \left(\frac{x}{2}\right)^5$
Calculate $2^5$: Expand the expression.$\newline$$f^{-1}(x) = \frac{x^5}{2^5}$
Write final expression: Calculate $2^5$.$\newline$$2^5 = 32$
Write final expression: Calculate $2^5$.$\newline$$2^5 = 32$ Write the final expression for the inverse function.$\newline$$f^{-1}(x) = \frac{x^5}{32}$