For the function f(x)=(3)/(9-2x), find f^(-1)(x). Answer: f^(-1)(x)=

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For the function  f(x)=(3)/(9-2x), find  f^(-1)(x). Answer:  f^(-1)(x)=

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Replace with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by replacing f(x) with y for clarity. y = (3)/(9 - 2x)Switch x and y: Now, switch x and y to find the inverse function. x = (3)/(9 - 2y)Cross-multiply to eliminate fraction: Next, we solve for y. To do this, we'll first cross-multiply to get rid of the fraction. x * (9 - 2y) = 3Distribute x: Distribute x into the parentheses. 9x - 2xy = 3Isolate term with y: We want to isolate the term with y, so let's move the term without y to the other side by subtracting 9x from both sides. -2xy = 3 - 9xDivide by -2x: Now, divide both sides by -2x to solve for y. y = (3 - 9x) / (-2x)Factor out -3: We can simplify the expression by factoring out a -3 from the numerator. y = -3(1 + 3x) / (-2x)Cancel negative signs: The negative signs in the numerator and denominator cancel each other out. y = 3(1 + 3x) / (2x)Write inverse function: Finally, we can write the inverse function by replacing y with f^(-1)(x). f^(-1)(x) = 3(1 + 3x) / (2x)

For the function $f(x)=\frac{3}{9-2 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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For the function f(x)=39−2x f(x)=\frac{3}{9-2 x} f(x)=9−2x3​, find f−1(x) f^{-1}(x) f−1(x).\newlineAnswer: f−1(x)= f^{-1}(x)= f−1(x)=

For the function $f(x)=\frac{3}{9-2 x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$