Question

given that f(x)=-9x+3 and g(x)=x^4, find (f.g)(x) and its domain

Answer 1

Just as clarification of notation:
Does:
\[(f.g)(x)=f(g(x))\]

Answer 2

no its like (fog)(x)

Answer 3

its like that but i cant get it on the keyboard

Answer 4

help mepls

Answer 5

Ahhh, I see, you are looking for f of g of x. This can be written as below.
\[f(g(x))\]


We can also write this as f(x) where we let x = g(x):
\[f(x)\]
So substitute in x = g(x)
\[f(g(x))\]

Now we'll try this working with your functions.
So we have:
\[f(x)=-9x+3\]
Now we need to let x = g(x)
So:
\[x=x^4\]
Now we substitute this new value for x in to the function for f(x) to give our final answer:
\[f(g(x))=-9x^4+3\]

Helpful?

Answer 6

not really can you give me the answer

Answer 7

Okay, you think you can substitute the value of g(x) into f(x) as if it was just an x value. That will give you the answer and if you look at my working above I have done the answer.
Is there anything in particular that you don't understand about my explanation? :)

Answer 8

oh so you just put x^4 into the 9x right?

Answer 9

Yeah, you substitute it in as if it was an x value. It can get quite a bit harder than that though :)

Answer 10

whats the domain then?

Answer 11

The domain would be real numbers because it's just a quartic function

Answer 12

infinity, negative infinity?

Answer 13

Yep, when you think about the function there is no number you can give it that won't return a real answer back.

Answer 14

i have so many more questions

Answer 15

You can close this question and open another one if you would like to ask another question. I'll keep a look out for it :)