How do you find #(gof)(x)# given #f(x)=-3x+7# and #g(x)=x^2-8#?

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Answer 1 · 2017-05-20T13:40:52

#(g@f)(x)=9x^2-42x+41#

To make it a bit more obvious what is happening:

Set #f(x)=z=-3x+7#

#g(z)=z^2-8#

So by substitution:

#(g@f)(x)->g(z)=(-3x+7)^2-8#

#(g@f)(x)=9x^2-42x+49-8#

#(g@f)(x)=9x^2-42x+41#

Answer 2 · 2018-08-05T01:42:04

#g(f(x))=(-3x+7)^2-8#

We have the composite function #g(f(x))#. Notice that #f(x)# is the inside function, so we can plug this into #g(x)#. We get

#color(steelblue)(f(x)=-3x+7)#

#color(purple)(g(x)=x^2-8)#

#color(purple)(g(color(steelblue)(f(x)))=(color(steelblue)(-3x+7))^2-8#

Hope this helps!