Question

Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work. I put them together for (2x2+5)2+( 2x2+5)+2. Now I'm stuck.

Answer 1

I think you just simplify now, remember for \[(a + b)^2 = a^2 + 2ab + b^2\]

Answer 2

so try and simplify and post up what you get

Answer 3

Alright

Answer 4

I'm still confused. the exponents are what I don't understand. Do I add the terms together or...

Answer 5

yup you want to add like terms together. have you tried expanding \[(2x^2 + 5)^2\]?

Answer 6

Expanding?

Answer 7

because it best if you have a go and I can then check and direct you

Answer 8

Yup you can expand/open them using the rule I'd shown you above

Answer 9

then we can collect like terms to simplify

Answer 10

Oh! Ok. Got it. Hold on a moment.

Answer 11

I got \[2x ^{4}+5^{2}+2x ^{2}+7\] Is that all I can do? Or can it be simplified more?

Answer 12

hm your answer doesn't quite match mine, what did you get when you expanded \[(2x^2 + 5)^2\]?

Answer 13

\[2x ^{4}+5^{2}\]

Answer 14

OH!

Answer 15

5squared should be 25.

Answer 16

not quite, so we have \[(2x^2 + 5)^2\] and using \[(a + b)^2 = a^2 + 2bc + b^2\]
we should get \[(2x^2)^2 + 2(2x^2)(5) + 5^2\]
which simplifies down to \[4x^4 + 20x^2 + 25\] when we expand

Answer 17

Is That all we can do?

Answer 18

no, we'e simplified the \[(2x^2 + 5)^2\] part, but don't forget, our task is to simplify \[(2x^2 + 5) + (2x^2 + 5) + 2\] so now we have \[4x^4 + 20x^2 + 25 + (2x^2 + 5) + 2\] so now you gotta collect like terms, try this and show me what you get @Whitelynx

Answer 19

sorry correction from above****
"Our task is to simplify \[(2x^2 + 5)^2 + (2x + 5) + 2\]"****

Answer 20

\[4x ^{4}+22x ^{2}+32\]
Is this right?

Answer 21

yupp thats correct @whitelynx! :D