Question

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

Answer 1

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.