Question

I know the answer is either A or B , just confused

Answer 1

Let's try Choice A

first, write down G(x)
\[G(x) = x^2\]
now replace all the x's with F(x)
what do you get ?

Answer 2

G(F(x))=F(x)^2

Answer 3

and we have to remember that F(x)^2 means (F(x) ) ^2
next we replace F(x) with 3x+1
we get
\[ G(F(x)) = (3x+1)^2 \]

Answer 4

I assume you know
(3x+1)^2 is not the same as 3x^2+1

Answer 5

Yes so step one is to substitute all x's with f(x)
Then you take out the f(x) and substitute the equation given

Answer 6

Yes I do know that

Answer 7

ok, so choice A does not work.

Answer 8

Okay let me try choice b

Answer 9

G(F(x))=3x^2 right?

Answer 10

The first step should be
G(x) = 3x^2
becomes
G(F(x) ) = 3(F(x))^2

now do the 2nd step

Answer 11

G(x)=x+1^2

Answer 12

G(F(x))=x+1^2

Answer 13

ok, but you left out the 3 and you should have parens around x+1 (it's one thing)
try again

Answer 14

G(F(x))=(3x+1)^2

Answer 15

Like that?

Answer 16

almost. F(x) is (x+1)
the 3 belongs "outside"

Answer 17

G(F(x))=3(x+1)^2

Answer 18

yes. looks good, but it's not the answer we want.

Answer 19

Choice d then =)

Answer 20

I did it here on paper

Answer 21

yes, choice D

fyi, choice C gives
G(F(x)) = 1
which is not what we want.