Domain

May 2010
22
10
sin(x) is defined for all real numbers, so are sin(3x) and -4sin(3x)
 
Last edited:

Grandad

MHF Hall of Honor
Dec 2008
2,570
1,416
South Coast of England
Hello winsome

Do you understand what is meant by the word domain of a function? It is the set of valid inputs to that function. For example, the domain of \(\displaystyle \sqrt x\) is the set of non-negative numbers.

Now, as papex has said, \(\displaystyle \sin x\), and therefore \(\displaystyle \sin3x\) and \(\displaystyle -4\sin 3x\), are defined for all values of \(\displaystyle x\). In other words, the domain of these functions is the set of all real numbers.

There are various ways of writing this set. One is to use the symbol \(\displaystyle \mathbb{R}\). Another is to use interval notation: \(\displaystyle (-\infty, +\infty)\).

Grandad