SOLUTION: If f(x) = 2x + 4, and g(x) = (x^2 + x + 5), find g (f(x)).

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Question 551096: If f(x) = 2x + 4, and g(x) = (x^2 + x + 5), find g (f(x)).
Answer by mathstutor458(57) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 2x + 4, and g(x) = (x^2 + x + 5)
g (f(x)) = g(2x+4) (substituted f(x)=2x+4 )
g(x) = (x^2 + x + 5)
g(2x+4) means instead of x we have to substitute 2x+4 in g(x)
g(2x+4)=(2x+4)^2+(2x+4)+5
we know the formula,(a+b)^2=a^2+2ab+b^2
here a=2x,b=4
g(2x+4)=(2x+4)^2+(2x+4)+5
=(2x)^2+2(2x)(4)+(4)^2+2x+9 (since,4+5=9)
=4x^2+16x+16+2x+9 (since,(2x)^2=4x^2,2(2x)(4)=16x)
=4x^2+18x+25 --->answer (since,16x+2x=18x,16+9=25)