Question

Consider the following functions.

f(x) = 4/x, g(x) = x/(x + 4)
Find (fºg) (x).
Find the domain of (fºg) (x) . (Enter your answer using interval notation.)
Find (gºf) (x) .

Answer 1

`f(g(x)) = f( (x)/(x + 4) ) = (4)/( (x)/(x + 4) ) = (4(x + 4))/(x)`

Domain of f(g(x)):

(-infinity, -4) U (-4, 0) U (0, 4)

`g(f(x)) = g ( (4)/(x) ) = ( (4)/(x) )/( (4)/(x) + 4 ) = (4)/(4x + 4) = 4( (1)/(x + 1) )`

Domain of g(f(x)):

(-infinity, 0) U (0, infinity)