Given #f(x) = 2x^3 + x^2# and #g(x) = 7x - 2# how do you find (gf)(3)?

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Answer 1 · 2018-05-23T20:19:47

#g(f(3))=439#

To find #g(f(3))#, we need to find #g(f(x))# first.

#g(x)# is our outside function, so we'll start with that first.

#color(blue)(g(x)=7x-2)#

Wherever we see an #x#, we'll replace it with #color(red)(f(x))#. We get

#g(f(x))=color(blue)(7color(red)((2x^3+x^2))-2#

which further simplifies to

#g(f(x))=14x^3+7x^2-2#

To find #g(f(3))#, we just have to plug #3# in for #x#. We get

#g(f(3))=14(3)^3+7(3)^2-2#

#=>=14(27)+7(9)-2#

#=>=378+63-2#

#=>441-2#

#g(f(3))=439#

Hope this helps!