Finding the domain of a composite function

Hi guys I am seriously confused !!!

So basically I would like to know how to find the domain of a composite function. After watching some YouTube videos the general rule seems to be that you must find what x cannot be for the inside function and then do the same for the composite function.

I have attached a copy of the question

So from g(x) x cannot equal 1 or -1 and from the composite function x cannot equal +/- 1/2

Now how on earth do I answer the question :confused:

Original post by Olive123

Hi guys I am seriously confused !!!

So basically I would like to know how to find the domain of a composite function. After watching some YouTube videos the general rule seems to be that you must find what x cannot be for the inside function and then do the same for the composite function.

I have attached a copy of the question

So from g(x) x cannot equal 1 or -1 and from the composite function x cannot equal +/- 1/2

Now how on earth do I answer the question :confused:

That's an appallingly worded question. There is literally no correct way to answer it, since they don't tell you what the initial domains of

f

and

g

. Assuming that they are both functions on the largest subset of

\mathbb{R}

for which they take real values, in the former case, you are correct that, under that assumption, the domain of

fg

is a subset of

\mathbb{R}\setminus \{1,-1\}

. However, note that, under that assumption, the interior of any square roots must be non-negative.

Reply 2

ztibor

10

Original post by Olive123

Hi guys I am seriously confused !!!

So basically I would like to know how to find the domain of a composite function. After watching some YouTube videos the general rule seems to be that you must find what x cannot be for the inside function and then do the same for the composite function.

I have attached a copy of the question

So from g(x) x cannot equal 1 or -1 and from the composite function x cannot equal +/- 1/2

Now how on earth do I answer the question :confused:

for f(x)