Find the inverse function of the function f(x)=(5x)^(-(9)/(5)) on the domain x > 0. f^(-1)(x)=((x)/(5))^((5)/(9)) f^(-1)(x)=(x^(-(5)/(9)))/(5) f^(-1)(x)=((x)/(5))^(-(5)/(9)) f^(-1)(x)=(x^((5)/(9)))/(5)

Write function as y: To find the inverse function, we first write the function as y = (5x)^(-(9)/(5)).Swap x and y: Next, we swap x and y to find the inverse function, so we have x = (5y)^(-(9)/(5)).Solve for y: Now, we solve for y. To do this, we raise both sides of the equation to the power of -(5/9) to get rid of the negative exponent on the right side. This gives us x^(-(5)/(9)) = 5y.

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Find the inverse function of the function
f(x)=(5x)^(-(9)/(5)) on the domain
x > 0.

f^(-1)(x)=((x)/(5))^((5)/(9))

f^(-1)(x)=(x^(-(5)/(9)))/(5)

f^(-1)(x)=((x)/(5))^(-(5)/(9))

f^(-1)(x)=(x^((5)/(9)))/(5)

Find the inverse function of the function $f(x)=(5 x)^{-\frac{9}{5}}$ on the domain x>0 . $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{\frac{5}{9}}$ $\newline$ $f^{-1}(x)=\frac{x^{-\frac{5}{9}}}{5}$ $\newline$ $f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{5}{9}}$ $\newline$ $f^{-1}(x)=\frac{x^{\frac{5}{9}}}{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=(5 x)^{-\frac{9}{5}}

on the domain

x>0

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{\frac{5}{9}}

\newline

f^{-1}(x)=\frac{x^{-\frac{5}{9}}}{5}

\newline

f^{-1}(x)=\left(\frac{x}{5}\right)^{-\frac{5}{9}}

\newline

f^{-1}(x)=\frac{x^{\frac{5}{9}}}{5}

Write function as $y$ : To find the inverse function, we first write the function as $y = (5x)^{-\frac{9}{5}}$ .
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function, so we have $x = (5y)^{-(\frac{9}{5})}$ .
Solve for y: Now, we solve for $y$ . To do this, we raise both sides of the equation to the power of $-\left(\frac{5}{9}\right)$ to get rid of the negative exponent on the right side. This gives us $x^{-\left(\frac{5}{9}\right)} = 5y$ .