j(x)= x/2x+3?

Question

find the inverse

Answer 1

This usually means, solve for x in terms of y
Let y = j(x) = x/(2x+3)
y = x/(2x+3)
(2x+3)/x = 1/y
2 + 3/x = 1/y
3/x = 1/y - 2 = (1-2y)/y
x = 3y/(1-2y)

so, x = 3j(x)/(1-2j(x))

Answer 2

let y = x/(2x+3), then interchange x and y
x = y/(2y+3) and solve for y.
2xy + 3x = y
y - 2xy = 3x
y(1 - 2x) = 3x
y = 3x/(1 - 2x)

notice the original has a horizontal asymptote at y = 1/2, and the inverse has a vertical asymptote at x = 1/2, which is the symmetry over y=x that an inverse must have. Similarly for the original vertical asymptote at x = -3/2 and the inverse's horizontal at y = -3/2.

Answer 3

i think its 2/3 but im not completely positive.

Answer 4

-3.5