F(x)=1/2x; g(x)=1/3x find f(g(x) and g(f(x) State domain of each Precalculus questions?

Defining New functions Algebraicially

1 Answer
Sep 17, 2016

#f(g(x))=1/6x# and #g(f(x))=1/6x#. The domain is #(-oo,oo)#.

Explanation:

#f(x)=1/2x# and #g(x)=1/3x#

To find #f(g(x))#, plug #g(x)# into #f(x)#

#f(g(x))=1/2(1/3x) =1/6x#

To find #g(f(x))#, plug #f(x)# into #g(x)#

#g(f(x))=1/3(1/2x)=1/6x#

The domain of #1/6x# is #(-oo,oo)# because f(x) is defined for all values of x.