Find: g(f(h(-3))) f(x) = 2x g(x) = -3x+4 h(x) = 2x-8

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Given f(x)=2x,g(x)=-3x+4, and h(x)=2x-8 find g(f(h(-3))):

(1) One way is to evaluate from the inside out:

h(-3)=2(-3)-8=-14

f(-14)=2(-14)=-28

g(-28)=-3(-28)+4=88

So g(f(h(-3)))=88

(2) Another way is to find the expression for g(f(h(x))) and substitute -3 for x:

h(x)=2x-8

f(h(x))=2(2x-8)=4x-16

g(f(h(x)))=-3(4x-16)+4=-12x+52

So g(f(h(-3)))=-12(-3)+52=36+52=88 as before.

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