f(x) essentially is y, so the equation now reads x=(3y)/(y+1)

you then multiply each side by (y+1) getting xy + x=3y

then divide by three to get (xy/3) + (x/3)=y

The functions f and g are inverse functions if f(g(x)) = x for all x in the domain of g and g(f(x)) = x for all x in the domain of f.

The inverse of a function f is usually denoted f –1 and read “f inverse.” (Note that the superscript –1 in f –1 is not a exponent).

Suppose that two functions are inverses. If (a, b) is a point on the graph of the original function, then the point (b, a) must be a point on the graph of the inverse function. The graphs are mirror images of each other with respect to the line y = x.

To find the inverse of a function algebraically, interchange the x and y and solve for y.

Example:

Let h(x) = x3 + 4

Replace h(x) with y and interchange x and y:

y = x3 + 4

x = y3 + 4

Solve for y: x – 4 = y3