SOLUTION: Find the domain and range of the composite function f o g, g o f f(x)=1/x g(x)=x/(x+1)

Question 785657: Find the domain and range of the composite function
f o g, g o f
f(x)=1/x
g(x)=x/(x+1)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the domain and range of the composite function
f(x)=1/x
g(x)=x/(x+1)
---------------
f o g = f[g(x)] = f[x/(x+1)] = (x+1)/x = 1+(1/x)
Domain:: All Real numbers except x = 0
Range: All Real numbers except y = 1
=======================================
g o f = g[f(x)] = g[1/x] = (1/x)/((1/x)+1) = (1/x)/(1+x)/x = 1/(1+x)
Domain: All Real Numbers except x = -1
Range:: All Real Numbers except y = 0
==========================================
Cheers,
Stan H.
===================

RELATED QUESTIONS
Find the domain of the composite function f o g. f(x)= x/x+3 ; g(x)=9/x+1 (answered by josgarithmetic)

For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o... (answered by rothauserc)

Find: a.) F o G b.) G o F c.) F o F d.) G o G also find the domain of each composite (answered by stanbon)

Find the domain of the composite function f o g f(x)= square root x; g(x)=... (answered by chessace)

find the domain of the composite function f o g f(x)= square root 2-x; g(x) = {2x-1} (answered by MRperkins)

Please help find the domain of the composite function f o g f(x) = √2-x - 3;... (answered by stanbon)

Find the domain of the composition function f o g F(x) = 1/ x-9 ; g(x) = 1/x (answered by stanbon)

f(x)=(5)/(x+4), g(x)=(1)/(x) find (f o g)(x) and the domain of f o g (answered by solver91311)

Given f(x)= 3 over x(squared)-4 and g(x)= 5 over x Find the following 1. f o g... (answered by MathLover1)