Question 669151

Hello,
I have been trying for hours to help my son with his Algebra I homework and I am stuck on one problem.  The problem is this:
If f(x)=4x-2 and g(x)=x^2+2, then find the following g(2)=________

This is what I have done thus far:
1. f(g(1))
g(1)=1^2+2 (1)
g(1)=3

f(g(1))=f(3)
f(3)=4(3)-2
f(3)=12-2
f(g(1))=10

2. g(f(1))
f(1)=4(10)-2
f(1)=40-2
f(1)=8

g(f(1)=g(38)
g(38)=38^2-2(1)
g(38)=76-2
g(38)=74

3. f(g(x))=f(x^2+2x)
    f(x^2+2)=4(x^2+2x)-2=8x^2+8x-2
Is this correct? 


If f(x) = 4x-2 and g(x) = {{{x^2 + 2}}}, then find the following g(2)=________


g(2) = {{{2^2 + 2}}}, or g(2) = {{{highlight_green(6)}}}


No. 1 is CORRECT!!


1. f(g(1))
g(1)=1^2+2 (1)
g(1)=3


f(g(1))=f(3)
f(3)=4(3)-2
f(3)=12-2
f(g(1))=10


No. 2 is INCORRECT!!


f(x ) = 4x - 2 and g(x) = {{{x^2 + 2}}}


2. g(f(1))
f(1) = 4(1) - 2
f(1) = 4 - 2
f(1) = 2


g(f(1)) = g(2) = {{{2^2 + 2}}}, or g(f(1)) = g(2) = {{{highlight_green(6)}}}


No. 3 is INCORRECT!!


f(x) = 4x - 2 and g(x) = {{{x^2 + 2}}}


3. f(g(x)) = f({{{x^2 + 2}}})
f({{{x^2 + 2}}}) = {{{4(x^2 + 2) - 2}}}, or f(g(x)) = f({{{x^2 + 2}}}) = {{{highlight_green(4x^2 + 6)}}}


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