find the inverse of: f(x)=(2x-3)/(x+1)  and state its domain

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f(x) = (2x - 3) / (2x + 1) y = (2x - 3) / (2x + 1) (express f(x) as y) Switch x's and y's for inverse: x = (2y - 3) / (2y + 1) Solve for y: x(2y + 1) = 2y - 3 (cross multiply) 2xy + x = 2y - 3 (distribute x on left side) 2xy + x - 2y = -3 (get rid of 2y on right side) 2xy - 2y = -x - 3 (get rid of x on left side) y(2x - 2) = -x - 3 (factor out y on left side) y(2x - 2) = -1(x + 3) (factor out -1 on right side) y = (-1(x + 3)) / (2x - 2) (get rid of 2x - 2 on left side) y = (-1(x + 3)) / (2(x -1)) (factor out 2 in denominator on left side) Inverse Function (express y as f(x)): f(x) = (-1(x + 3)) / (2(x - 1)) Domain is x not = 1, since x = 1 causes division by zero, which makes inverse function undefined.