Let #f(x) = (1) / (1-3x) # and #g(x) = (1) / (x^2) # how do you find f(g(x)?

1 Answer
Oct 23, 2015

Put #g(x)# in place of #x# in the formula for #f(x)# and simplify to find:

#f(g(x)) = 1+3/(x^2-3)#

Explanation:

#f(g(x))#

#= 1/(1-3g(x))#

#= 1/(1-3(1/(x^2)))#

#= x^2/(x^2-3)#

#= (x^2-3+3)/(x^2-3)#

#= 1+3/(x^2-3)#

with restriction #x != 0#

The restriction is necessary because #g(x)# is undefined for #x = 0#, but #1+1/(x^2-3)# is normally defined when #x = 0#.