Find the inverse of this function?

Switch x and y and solve for y. x=(2y-5)/(y+3). xy+3x=2y-5 and xy-2y=-3x-5 and y(x-2)=-(3x+5) and we have y=(3x+5)/(2-x). We change x-2 to 2-x to get rid of the (-) sign on the right side.

To find the inverse of a function, you want to take the original function (y=2x - 5 / x + 3) and switch the positions of x and y. Then, you need to solve for y. Whatever you get is the inverse of the function! This problem seems a little tough.... I'll try to show you how to do it... or at least how to start it:

y = 2x-5 / x+3 switch x and y

x = 2y-5 / y+3 multiply both sides by y+3

x(y+3) = 2y-5 distribute the x to the y+3

xy + 3x = 2y-5 add 5 to both sides

xy + 3x + 5 = 2y multiply both sides by 1/2

1/2(xy + 3x + 5) = y distribute the 1/2 to the part in ( )

1/2xy + 3/2x + 5/2 = y divide both sides by y

1/2x + 3/2x + 5/2 = y/y add the two x-numbers together

4/2x + 5/2 = y/y multiply both sides by y (and simplify)

(2x + 5/2)y = y ...i hate math xD

You could also find the inverse by just looking at the function and making everything inverted:

y = 2x-5 / x+3

the inverse of a number is the number raised to the -1 power, or 1 over that number (i.e. if it was 4, the inverse of 4 is 1/4)

y = 1/2x -1/5 / 1/x + 1/3 multiply numerator by reciprocals of denominator

y = [1/2x -1/5]*[x/1 + 3/1]

uhg... I hope I didn't confuse you... I know how to do inverses, it's a bit hard for me to actually do the math (lol that won't get me best answer xD)

x = (2*y - 5)/(y + 3)

f^-1(y) = - (3*x + 5)/(x - 2)

y = (2x - 5)/(x + 3)

= (2(x + 3) - 11)/(x + 3)

= 2 - (11/(x + 3))

11/(x + 3) = 2 - y

x + 3 = 11/(2 - y)

x = (11 - 3(2 - y))/(2 - y)

= (5 + 3y)/(2 - y)

This is the inverse.

y= 2x-5 / x+3

=> yx +3y = 2x - 5

=> yx - 2x = - 3y - 5

=> x (y - 2) = - ( 3y + 5)

=> x = (3y + 5) / (2 - y)