Question

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

Answer 1

@Vocaloid I just need to learn how to do the problem, not the answer.

Answer 2

replace x in f(x) function by g(x)

Answer 3

I did that, I got: (2x^2+5)^2+2x^2+2

Answer 4

you forgot something \[ \huge\rm (2x^2+5)^2+\color{blue}{x}+2\]
x = 2x^2 + 5

Answer 5

you forgot 5

Answer 6

did I? Sorry.

Answer 7

So to solve, is it 2x^4 or 4x^4

Answer 8

\[ \huge\rm (2x^2+5)^2+\color{blue}{2x^2 +5}+2\]

Answer 9

\[ \huge\rm \color{reD}{x^2}+\color{blue}{x}+2\]
\[ \huge\rm \color{ReD}{(2x^2+5)^2}+\color{blue}{2x^2 +5}+2\]
x is 2x^2 + 5

Answer 10

Yes, so now we have to square x.

Answer 11

yes( 2x^2 +5)^2 is same as (2x^2 +5) (2x^2 +5) so foil it

Answer 12

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

Answer 13

right?

Answer 14

yes that's right

Answer 15

So now we combine like terms?

Answer 16

yesp

Answer 17

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

Answer 18

turns into

Answer 19

\[4x^4+22x^2+32\]

Answer 20

Right?

Answer 21

yep

Answer 22

So now I need to factor?

Answer 23

nope that's ur answer

Answer 24

Oh, is it? Good, my problem was I tried factoring that and had no idea how to do it.

Answer 25

Thanks! :D

Answer 26

my pleasure
and yes that's it
they wants us to find f(g(x)) not factoring

Answer 27

I fanned, so if I need anything, I'll make sure to tag you.

Answer 28

thanks i'll try my best :=)

Answer 29

@Nnesha I have one more problem that seems pretty easy.

Answer 30

I think I may know how to solve it but graphing and radicals are my weakpoint.

Answer 31

Describe how to transform \[(\sqrt[6]{x ^{5}})^{7}\] into an expression with a rational exponent

Answer 32

alright remember this exponent rule \[\huge\rm \sqrt[m]{x^n} = x^\frac{ n }{ m }\] you can convert root to exponent form

Answer 33

Yes I know this, it would be \[(x^\frac{ 5 }{ 6 })^7\]

Answer 34

then you multiply 7 and 5?

Answer 35

yep! right you already know

Answer 36

\[\huge\rm (x^m)^n = x^{ m \times n}\]

Answer 37

\[x^\frac{ 35 }{ 6 }\]

Answer 38

thats a 35/6 btw

Answer 39

yep

Answer 40

And that is my answer?

Answer 41

yep right

Answer 42

K, thanks. Just wanted to check my answer.

Answer 43

your answer is correct you're a mathematician :=)