Question

Let f(x) = 3x+1 and g(x) = x2
Find f(g(x))
Find g(f(x))

Answer 1

Of so the trick is to take one equation and put it in the place of x in the other equation...so...

Answer 2

so 3x+1=0 is what i do

Answer 3

No ok ... so f(x) = 3x+1 so f(3) means that you take 3 and put it where you saw an x right?
So f(3) = 3(3) +1

Answer 4

right?

Answer 5

oh ok i see

Answer 6

or in other words f(3) = 3(3)+1 = 10 so f(3) = 10

Answer 7

so for f(x) = 3x +1 and g(x) = x^2 ...

Answer 8

thats what i got

Answer 9

for f[g(x)] you have put g(x) in place of the x in f right? so put g(x) everywhere you saw x in f

Answer 10

so f(g(x)) = 3*[g(x)] + 1 ... see how I put g(x) where I saw x in the original f(x) =3x+1

Answer 11

i see

Answer 12

do i have to divide 3x by 3x and 1 by 3x?

Answer 13

Ok now last step replace the g(x) with what g(x) is which is x^2...

Answer 14

no, no division all this is is substitution and simplification.

Answer 15

so you have f(g(x))=(3) (g(x)) + 1 but now inplace of g(x) you will put x^2...so that gives you...

Answer 16

f(g(x)) = (3) (x^2) +1 but we would we normally don't put numbers multiplied by variables in parentheses so we would just write f(g(x))=3x^2 +1

Answer 17

that is the final answer the f(g(x)) = 3x^2+1

Answer 18

Now for g(f(x)) you start instead with g(x)...and g(x) = x^2 right?

Answer 19

yes
+

Answer 20

so now if you put f(x) in the belly of g(x) you have g(f(x))... that means where you saw x in g(x) = x^2 you have to put f(x) so what would that be?

Answer 21

g[3(x^2)]

Answer 22

No...look g(x) = x^2 so g(f(x)) = (f(x))^2 see how I just substituted f(x) where there was an x in the g function?

Answer 23

oh ok

Answer 24

but what is f(x) really?

Answer 25

f(3)

Answer 26

No Think about equals ... equals means is so if I write f(x) =3x+1 what I am saying is ... f(x) IS 3x+1... Like Bruce Wayne = Batman ... It means that Bruce Wayne really is Batman and vice versa...same thing in math. So if I write f(x) = 3x+1 what I am saying is that f(x) is actually just 3x+1 in disguise or f(x) is 3x+1 but by another name but reallly just the same thing.

Answer 27

so going back we had g(f(x)) = (f(x))^2 but what is f(x) really?

Answer 28

oh ok so its 3x+1

Answer 29

right so in g((fx)) = (f(x))^2 you replace the f(x) in the RIGHT hand side of the equation by (3x+1)... so go ahead and do that.

Answer 30

Show me what you have.

Answer 31

(3x+1)=[f(x)]^2

Answer 32

No no .... We had g(f(x)) = (f(x))^2... just substitute 3x+1 in place of the "f(x)" in the right hand side of the equation...remember substitute means remove one thing and replace it with a equivalent thing ... so in this case you are removeing "f(x)" from teh right hand side of the equation and replacing it with the equivalent thing "3x+1"

Answer 33

so your answer should start like this .... g(f(x)) = ...

Answer 34

I t would read "g of f of x is ..."