For the function f(x)=(9-5x)/(3+x), find f^(-1)(x). Answer: f^(-1)(x)=

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For the function  f(x)=(9-5x)/(3+x), 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 to make it easier to work with. y = (9 - 5x) / (3 + x)Interchange x and y: Now, interchange x and y to find the inverse function. x = (9 - 5y) / (3 + y)Multiply both sides: Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (3 + y) to eliminate the fraction. x(3 + y) = 9 - 5yDistribute x: Distribute x on the left side of the equation. 3x + xy = 9 - 5yMove terms with y: Now, we want to get all the terms with y on one side and the constant terms on the other side. Let's move the term with y on the left side to the right side by adding 5y to both sides. 3x + xy + 5y = 9Combine like terms: Combine like terms on the left side. 3x + y(x + 5) = 9Factor out y: To isolate y, we need to factor it out from the terms on the left side. y(x + 5) = 9 - 3xDivide both sides: Now, divide both sides by (x + 5) to solve for y. y = (9 - 3x) / (x + 5)Replace y with f^(-1)(x): We have found the inverse function. So, we can replace y with f^(-1)(x) to express our answer. f^(-1)(x) = (9 - 3x) / (x + 5)

For the function $f(x)=\frac{9-5 x}{3+x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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For the function f(x)=9−5x3+x f(x)=\frac{9-5 x}{3+x} f(x)=3+x9−5x​, find f−1(x) f^{-1}(x) f−1(x).\newlineAnswer: f−1(x)= f^{-1}(x)= f−1(x)=

For the function $f(x)=\frac{9-5 x}{3+x}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$