SOLUTION: Good Day! I would like to ask what is the inverse of the function {{{ g(x) = x/(x^2+1) }}} , if it exists.

Algebra ->  Functions -> SOLUTION: Good Day! I would like to ask what is the inverse of the function {{{ g(x) = x/(x^2+1) }}} , if it exists.      Log On


   

Question 995674: Good Day! I would like to ask what is the inverse of the function +g%28x%29+=+x%2F%28x%5E2%2B1%29+ , if it exists.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
y%2F%28y%5E2%2B1%29=x, and solve for y in terms of x?

g(x) is this:
graph%28300%2C300%2C-4%2C4%2C-4%2C4%2Cx%2F%28x%5E2%2B1%29%29
The inverse of g will not be a function.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+g%28x%29+=+x%2F%28x%5E2%2B1%29+ ....+g%28x%29+=y

+y+=+x%2F%28x%5E2%2B1%29+...........swap x and y
+x+=+y%2F%28y%5E2%2B1%29+....solve for y
+x%28y%5E2%2B1%29+=+y+
+xy%5E2%2Bx+=+y+
+xy%5E2-y%2Bx+=+0+
use quadratic formula:
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ..in your case a=x,b=-1, and c=x
y+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2Ax%2Ax+%29%29%2F%282%2Ax%29+
y+=+%281+%2B-+sqrt%28+1-4x%5E2+%29%29%2F%282x%29+
so, your inverse is:
g%5E-1%28x%29+=+%281%2B-sqrt%281-4x%5E2%29%29%2F%282x%29