Find the inverse function of the function f(x)=(2)/(9x). f^(-1)(x)=(9)/(2x) f^(-1)(x)=-(2)/(9x) f^(-1)(x)=(2)/(9x) f^(-1)(x)=-(9)/(2x)

Understand the problem: Understand the problem. We need to find the inverse function of f(x) = (2)/(9x). The inverse function, denoted as f^(-1)(x), is the function that reverses the effect of f(x). To find the inverse, we swap the roles of x and y in the original function and solve for y.Write with y: Write the original function with y. Let y = f(x), so we have y = (2)/(9x).Swap x and y: Swap x and y to find the inverse. Replace y with x and x with y to get x = (2)/(9y).Solve for y: Solve for y. To solve for y, we multiply both sides by 9y and then divide by x to isolate y. 9y * x = 2 y = 2 / (9x)Write inverse function: Write the inverse function. The inverse function is f^(-1)(x) = y, so we have f^(-1)(x) = 2 / (9x).

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Find the inverse function of the function
f(x)=(2)/(9x).

f^(-1)(x)=(9)/(2x)

f^(-1)(x)=-(2)/(9x)

f^(-1)(x)=(2)/(9x)

f^(-1)(x)=-(9)/(2x)

Find the inverse function of the function $f(x)=\frac{2}{9 x}$ . $\newline$ $f^{-1}(x)=\frac{9}{2 x}$ $\newline$ $f^{-1}(x)=-\frac{2}{9 x}$ $\newline$ $f^{-1}(x)=\frac{2}{9 x}$ $\newline$ $f^{-1}(x)=-\frac{9}{2 x}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=\frac{2}{9 x}

\newline

f^{-1}(x)=\frac{9}{2 x}

\newline

f^{-1}(x)=-\frac{2}{9 x}

\newline

f^{-1}(x)=\frac{2}{9 x}

\newline

f^{-1}(x)=-\frac{9}{2 x}

Understand the problem: Understand the problem. $\newline$ We need to find the inverse function of $f(x) = \frac{2}{9x}$ . The inverse function, denoted as $f^{-1}(x)$ , is the function that reverses the effect of $f(x)$ . To find the inverse, we swap the roles of $x$ and $y$ in the original function and solve for $y$ .
Write with y: Write the original function with y. $\newline$ Let $y = f(x)$ , so we have $y = \frac{2}{9x}$ .
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse. $\newline$ Replace $y$ with $x$ and $x$ with $y$ to get $x = \frac{2}{9y}$ .
Solve for y: Solve for y. $\newline$ To solve for y, we multiply both sides by $9y$ and then divide by $x$ to isolate $y$ . $\newline$ $9y \times x = 2$ $\newline$ $y = \frac{2}{9x}$
Write inverse function: Write the inverse function. $\newline$ The inverse function is $f^{-1}(x) = y$ , so we have $f^{-1}(x) = \frac{2}{9x}$ .