Question

@johnweldon1993

Let f(x) = x2 + x + 2 and g(x) = 2x2 + 5. Find f(g(x)). Show each step of your work.

Answer 1

I need to put the g(x) equation in every x of the f(x) equation... correct ?

Answer 2

correct

Answer 3

ok soo..

(2x^2 + 5)^2 + (2x^2 + 5) + 2

Answer 4

correct ?

Answer 5

mmhmm :)

Answer 6

\(\huge\color{green}{\checkmark}\)

Answer 7

and then combine like terms. this is where i get confused...

(2x^2 + 5)^2 + (2x^2 + 5) + 2

4x^4 goes first.. right.. cuz of 2x^2 and 2x^2 ?

Answer 8

Good so far!

Answer 9

there r two fives sooooo.... 4x^4 + 10

Answer 10

PEMDAS rule
parnetheses
exponent
then multipl or add subtract

Answer 11

parentheses**

Answer 12

Nope

So think of it like this

\[\large (2x^2 + 5)^2 \rightarrow (2x^2 + 5)(2x^2 + 5)\]

Answer 13

Follow the FOIL method...first, outside, inside, last

2x^2 times 2x^2 = 4x^4 <--we got that
now
2x^2 times 5 = 10x^2 right?

Answer 14

Basically you do the first term in the first parenthesis...and multiply it by every term in the second parenthesis....

Then take the second term in the first parenthesis..and multiply that by every term in the second parenthesis as well

So think of \(\large (2x^2 + 5)(2x^2 + 5)\) as \(\large 2x^2(2x^2 + 5) + 5(2x^2 + 5)\)

So that gives us

\[\large 4x^4 + 10x^2 + 10x^2 + 25\]
Then combine like terms...
\[\large 4x^4 + 20x^2 + 25\]

Good so far?

Answer 15

good... ish. lol

Answer 16

Lol no tell me what you dont get :)

Answer 17

That's the whole point of me being here :P

Answer 18

Okay so you get the reason why I wrote it like

\[\large (2x^2 + 5)(2x^2 + 5)\] right?

So what you did...was that first step I wrote from that...I rewrote the above as

\[\large \color \red{2x^2(2x^2} + 5) + 5(2x^2 + 5)\]

You did the first multiplication...*highlighted red above*

Now you just continue with the next multiplication *highlighted yellow this time*

\[\large \color \yellow{2x^2}(2x^2 + \color \yellow{5}) + 5(2x^2 + 5)\]

Answer 19

Okay yellow was a bad choice...but it works :P

Answer 20

oh ok got it

Answer 21

Mmhmm, so continue on and see if you can get to what I got :)

Answer 22

Okay good :)

So now for the rest

\[\large 4x^4 + 20x^2 + 25 + 2x^2 + 5 + 2\]

I'm sure you got this from here :)

Answer 23

Yeah sorry that's perfect :)