Domain vs Natural Domain (1 Viewer)

[HSC2014]

What is the difference between domain and natural domain? Is there any significance such that a question ask you to find the natural domain which would be different to finding the 'domain'?

 

[Carrotsticks]

Natural domain is the domain that the function has if I were to 'leave it naturally' by itself.

For example, the natural domain of y=ln(x) is x>0.

However, the domain of a function COULD be a domain that has been specified.

For example, the domain of y=ln(x) COULD be x>1 depending on how I wish to define it. This domain is considered 'unnatural' because I 'forced' a domain!

Another example is the sine function. It's natural domain is all real x, but the usual domain that we see it in is 0 < x < 2pi

 

[iBibah]

Natural domain is basically the x values for which the function is defined (not defined by the question, but defined by the function itself).

'Domain' or 'restricted domain' is 'man-made' you could say. It's placed by the question, or by a previous part to the question which established a restriction.

Example:

The function y=x has a natural domain all real x. But the question might say y=x for x>1. Now the 'domain' or 'restricted domain' is x is greater than 1.

If it said y=x, what's the domain, it means natural domain (unless a previous part established any restrictions).

EDIT: beaten by the man himself

 

[HSC2014]

Thank you both!

 

[asianese]

It sometimes also depends on how you write the function. For example, but in the first case since I wrote it like that then the natural domain would be . Or perhaps has a natural domain of even though you can write it has