Pre-calculus

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I want to make sure this is right.
the inverse of f(x)=(-3x+2)/(2x-1)
I got f^-1(x)=(x-2)/(2x-3).


if its right how do i check the answer to see if it is right. also would the domain of f be D=all real numbers except 1/2. And I do not know how to get the range for f^-1

  • Pre-calculus -

    y = (-3x+2) / (2x-1),
    x = (-3y+2) / 2y-1),
    Cross multiply:
    -3y + 2 = 2xy-x,
    -3y - 2xy = -x-2,
    y(-3-2x) = -x -2,
    y = (-x-2) / (-2x-3).

    -2x-3 = 0,
    -2x = 3,

    X = -3/2.

    Domain = All real values of X except
    -3/2.

    Range = All values of y resulting from inputs (x) within the domain.

    -Infinity < X < +Infinity.

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