If #f(x)=2x+8# and #g(x)=3x-2#, how do you find #g(f(-4))#?

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Answer 1 · 2018-04-07T15:38:44

#color(blue)(-2)#

First we find the function #g(f(x))#

To do this we substitute the variable #x# in #g(x)# for #f(x)#:

#:.#

#g(x)=3x-2#

#g(f(x))=3(f(x)-2#

#f(x)=2x+8#

So:

#g(f(x))=3(2x+8)-2=6x+24-2=6x+22#

We now plug in the value #x=-4#

#g(f(-4))=6(-4)+22=color(blue)(-2)#