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[comb yeah]

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[whys]

Your domain will be the intersection of g(x) and f(x)'s domains. So in this case, yes, it will be [-4pi, 4pi]. Try to visualise it - you can't exactly add the two values if one of the graphs ends and only one continues past a certain point.

For example, if two graphs, d(x) and t(x), had domains of (0,5] and [-1, 4) respectively, then the domain of d(x) + t(x) would be (0, 4) because this is the range of x-values for which both graphs are defined.

[comb yeah]

Your domain will be the intersection of g(x) and f(x)'s domains. So in this case, yes, it will be [-4pi, 4pi]. Try to visualise it - you can't exactly add the two values if one of the graphs ends and only one continues past a certain point.

For example, if two graphs, d(x) and t(x), had domains of (0,5] and [-1, 4) respectively, then the domain of d(x) + t(x) would be (0, 4) because this is the range of x-values for which both graphs are defined.

Thank you whys I get it now, so for both the functions, the domain would be -4pi to 4pi regardless if its addition or subtraction right?

[Sine]

Lately, I have been seeing an uptick on threads made in ALL CAPS and stuff like "HELP!!!".

I have changed the title of this thread but please try to refrain from those types of thread titles in the future.

[comb yeah]

Lately, I have been seeing an uptick on threads made in ALL CAPS and stuff like "HELP!!!".

I have changed the title of this thread but please try to refrain from those types of thread titles in the future.

Sorry, my bad!

[whys]

Thank you whys I get it now, so for both the functions, the domain would be -4pi to 4pi regardless if its addition or subtraction right?

For the first example on your main post, yes. Adding/subtracting doesn't change the fact that the domain is the intersection of the two functions.