SOLUTION: 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 fol

Algebra ->  Functions -> SOLUTION: 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 fol      Log On


   

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?
Found 2 solutions by ReadingBoosters, MathTherapy:
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with
f(x) = 4x -2
g%28x%29+=+x%5E2+%2B2
...
Find g(2)
(g(2)) = 2^2 + 2
= 4 + 2
g(2)= highlight_green%286%29
...
EDITED TO ADDRESS OTHER QUESTIONS
f(g(1)) =
start with g(1)
g(1) = 1^2 + 2
= 3
...
f(g(1) = 4(___) - 2
=4(3) - 2
= 12 - 2
f(g(1))= 10
...
g(f(1)) = (___)^2 + 2
start with f(1)
f(1) = 4(1) - 2
= 4 - 2
= 2
...
g(f(1)) = (___)^2 + 2
= 2^2 + 2
= 4 + 2
g(f(1)) = 6
...
f(g(x)) = 4(____) - 2
insert highlight%28g%28x%29%29
=4%28highlight%28x%5E2%2B2%29%29+-+2
Distribute the 4
=4x^2 + 8 - 2
f(g(x))=4x^2 + 6
.....
Delighted to help.
-Reading Boosters
Wanting for others what we want for ourselves.
www.MyHomeworkHelpers.com

Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

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%5E2+%2B+2, then find the following g(2)=________

g(2) = 2%5E2+%2B+2, or g(2) = highlight_green%286%29

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%5E2+%2B+2

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

g(f(1)) = g(2) = 2%5E2+%2B+2, or g(f(1)) = g(2) = highlight_green%286%29

No. 3 is INCORRECT!!

f(x) = 4x - 2 and g(x) = x%5E2+%2B+2

3. f(g(x)) = f(x%5E2+%2B+2)
f(x%5E2+%2B+2) = 4%28x%5E2+%2B+2%29+-+2, or f(g(x)) = f(x%5E2+%2B+2) = highlight_green%284x%5E2+%2B+6%29

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