Question

let f(x)=3x-4 and
g(x)=-x^2
evaluate the composite function (g*g)(2)

Answer 1

Do you mean (g o g)(x)?

Answer 2

uh yeah

Answer 3

It's the same as g( g(x) )

Answer 4

except the x says two

Answer 5

Yup, x is just a placeholder for any value.

Answer 6

i tried that but it gave me an answer that wasnt an option.

Answer 7

You tried \[(x ^{2})^{2}\] with x=2?

Answer 8

nope one sec

Answer 9

thank you

Answer 10

No problem. Here's a link that explains what's going on. One function basically becomes the input to a different function.

http://www.mathsisfun.com/sets/functions-composition.html

Answer 11

what if its (g o f)(0)

Answer 12

Did you read the link?

Answer 13

yeah but its still really confusing

Answer 14

(g o f)(x) becomes g( f(x) ). That means f(x) is the input for the function g. Once you have it in this form, just plug in zero for x.

Answer 15

If g(x) = 5x, then g(2)=5*2. And g(x+2)=5(x+2). Whatever is the input for a function just replaces the independent variables in the function.

Answer 16

so then if f(x)=3x-4 and g(x)=-x^2 then i would put -x^2(3x-4) and then input 0 for my x's?

Answer 17

in the end wouldnt the answer end up being 0?

Answer 18

No, in that you are simply multiply the expression together. You need to make f(x), which equals 3x-4, the input for g(x). You replace any x's in g(x) with whatever f(x) is, in this case 3x-4.

Answer 19

g(x) = x^2. We know that g(2) = (2)^2. And we know that g( x+2) = (x+2)^2. Do you see what is happening?

Answer 20

kind of

Answer 21

\[g(x)=x ^{2}\]\[g(2)=2^{2}\]\[g(x+2)=(x+2)^{2}\]

\[f(x)=3x-4\]\[g(f(x))=(f(x))^{2}\]\[g(3x-4)=?\]

Answer 22

3gx−4g? im not sure. and im sorry for asking all the questions. the system didnt teach me all this they only taut me the simple stuff

Answer 23

It's okay. I appreciate those willing to ask questions instead of just saying, "I don't get it."

Do you see how every time before we took what was in the parenthesis and squared it? That is what g(x) is, x^2.

So what we're doing now is the same thing; we take what's in the parenthesis and squaring it, because that is what g(x) is. So:

\[g(x)=x^{2}\]\[g(f(x))=g(3x-4)=(?)^{2}\]

Answer 24

i got g(3x-4)

Answer 25

\[g(x)=x^{2}\]\[g(f(x))=g(3x-4)=(3x-4)^{2}\]