Let #f(x) = x + 8# and #g(x) = 3x#, how do you find each of the compositions and domain and range?

1 Answer
Narad T.
Oct 22, 2016

The compositons are #f(g(x))=3x+8# Domain ∈#RR# Range ∈#RR#
and #g(f(x))=3x+24# Domain ∈#RR# Range∈ #RR#

Explanation:

#f(x)=x+8#

#g(x)=3x#

Replace x by 3x in g(x)
#fog(x)= f(g(x))=f(3x)=3x+8#
the domain is #RR#
and the range #RR#

Replace x by (x+8) in g(x)
#gof(x)=g(f(x))=g(x+8)=3(x+8)=3x+24#
the domain is #RR#
and the range #RR#

You can see that #f(g(x))!=g(f(x))#

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