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For the function f(x)=(3x-5)/(2x), find f^(-1)(x). Answer: f^(-1)(x)=

For the function f(x)=3x−52x f(x)=\frac{3 x-5}{2 x} , find f−1(x) f^{-1}(x) .\newlineAnswer: f−1(x)= f^{-1}(x)=

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Q. For the function f(x)=3x−52x f(x)=\frac{3 x-5}{2 x} , find f−1(x) f^{-1}(x) .\newlineAnswer: f−1(x)= f^{-1}(x)=
  1. Prepare for finding inverse: Set f(x)f(x) equal to yy to prepare for finding the inverse function.\newliney=3x−52xy = \frac{3x - 5}{2x}
  2. Swap xx and yy: Swap xx and yy to find the inverse function. This means we replace yy with xx and xx with yy in the equation.\newlinex=3y−52yx = \frac{3y - 5}{2y}
  3. Clear fraction and solve: Solve for yy. To do this, we need to clear the fraction by multiplying both sides of the equation by 2y2y.2xy=3y−52xy = 3y - 5
  4. Get terms on one side: Get all terms containing yy on one side of the equation and the constant term on the other side.2xy−3y=−52xy - 3y = -5
  5. Factor out yy: Factor out yy from the left side of the equation.y(2x−3)=−5y(2x - 3) = -5
  6. Divide to solve for y: Divide both sides of the equation by (2x−3)(2x - 3) to solve for y.\newliney=−5(2x−3)y = \frac{-5}{(2x - 3)}
  7. Replace with inverse function: Replace yy with f−1(x)f^{-1}(x) to denote the inverse function.f−1(x)=−52x−3f^{-1}(x) = \frac{-5}{2x - 3}

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