Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work.
Help please

Question

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work.
Help please

anonymous · Answer

@marihelenh can you help me with this one too?

anonymous · Answer

@freckles

marihelenh · Answer

You would replace what you have for f(x) into the x position of g(x).

$$\left( 4x ^{2}+x+1 \right)^{2}-2$$

Does that make sense?

anonymous · Answer

but where does the x^2-2 go

anonymous · Answer

the -2 is there but the x^2 i only see the ^2 added but not the x

marihelenh · Answer

The f(x) becomes a function of g(x), so you just replace what f was equal to into wherever the x is in the g equation.

anonymous · Answer

oh i think i get it

anonymous · Answer

yes i get it :D

marihelenh · Answer

Ok great! It is a little difficult trying to explain on here sometimes.

anonymous · Answer

4x^4+x^3-1  would this be the final answer?

anonymous · Answer

@marihelenh

marihelenh · Answer

Just one sec, let me check.

marihelenh · Answer

No, the answer is actually even longer.

marihelenh · Answer

To find the answer you would have to do,
$$(4x ^{2}+x+1)(4x ^{2}+x+1) -2$$

anonymous · Answer

This is so hard, i thought i understood but now i don't.

marihelenh · Answer

Do you have to simplify it?

anonymous · Answer

It says Find g(f(x)) so I think I have to but maybe not

marihelenh · Answer

Well, if you don't have to, you already have your answer, but I will help you simplify it. Just hang in with me. It will seem confusing, but we will get through it and to the answer. OK?

anonymous · Answer

ok, thank you

marihelenh · Answer

The first thing you should do, is multiply the first term of the first set by the second set.
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