Find the inverse function of the function f(x)=-(8x)/(9). f^(-1)(x)=(8x)/(9) f^(-1)(x)=-(9x)/(8) f^(-1)(x)=(9x)/(8) f^(-1)(x)=-(8x)/(9)

Understand Inverse Function: Understand the concept of an inverse function. The inverse function of f(x), denoted as f^(-1)(x), is a function that reverses the effect of f(x). If f(x) takes an input x and produces an output y, then f^(-1)(x) takes y as an input and produces the original x as an output. To find the inverse function, we need to solve the equation y = -(8x)/(9) for x in terms of y.Write Original Function: Write the original function with y as the output. Let y = f(x), so we have: y = -(8x)/(9)Swap x and y: Swap x and y to find the inverse function. To find the inverse, we switch the roles of x and y, so we get: x = -(8y)/(9)Solve for y: Solve for y in terms of x. Now we need to solve the equation for y: x = -(8y)/(9) Multiply both sides by -9/8 to isolate y: y = (-9/8)xWrite Inverse Function: Write the inverse function. The inverse function, f^(-1)(x), is then: f^(-1)(x) = (-9/8)x

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Find the inverse function of the function
f(x)=-(8x)/(9).

f^(-1)(x)=(8x)/(9)

f^(-1)(x)=-(9x)/(8)

f^(-1)(x)=(9x)/(8)

f^(-1)(x)=-(8x)/(9)

Find the inverse function of the function $f(x)=-\frac{8 x}{9}$ . $\newline$ $f^{-1}(x)=\frac{8 x}{9}$ $\newline$ $f^{-1}(x)=-\frac{9 x}{8}$ $\newline$ $f^{-1}(x)=\frac{9 x}{8}$ $\newline$ $f^{-1}(x)=-\frac{8 x}{9}$

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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)=-\frac{8 x}{9}

\newline

f^{-1}(x)=\frac{8 x}{9}

\newline

f^{-1}(x)=-\frac{9 x}{8}

\newline

f^{-1}(x)=\frac{9 x}{8}

\newline

f^{-1}(x)=-\frac{8 x}{9}

Understand Inverse Function: Understand the concept of an inverse function. The inverse function of $f(x)$ , denoted as $f^{-1}(x)$ , is a function that reverses the effect of $f(x)$ . If $f(x)$ takes an input $x$ and produces an output $y$ , then $f^{-1}(x)$ takes $y$ as an input and produces the original $x$ as an output. To find the inverse function, we need to solve the equation $y = -\frac{8x}{9}$ for $x$ in terms of $y$ .
Write Original Function: Write the original function with $y$ as the output. $\newline$ Let $y = f(x)$ , so we have: $\newline$ $y = -\frac{8x}{9}$
Swap $x$ and $y$ : Swap $x$ and $y$ to find the inverse function. $\newline$ To find the inverse, we switch the roles of $x$ and $y$ , so we get: $\newline$ $x = -\frac{8y}{9}$
Solve for y: Solve for y in terms of x. $\newline$ Now we need to solve the equation for y: $\newline$ $x = -\frac{8y}{9}$ $\newline$ Multiply both sides by $-\frac{9}{8}$ to isolate y: $\newline$ y = \left(-\frac{$9$}{$8$}\right)x
Write Inverse Function: Write the inverse function.\(\newlineThe inverse function, $f^{-1}(x)$ , is then: $\newline$ $f^{-1}(x) = \frac{-9}{8}x$