Domains of functions

The domain is the range of values the function can act upon, the input values to the function, or the x-values if y=f(x).

If a function is defined with an expression there are some things to look out for which could cause the domain to be restricted:

• Dividing by 0 - this is most likely to occur just at isolated points
• square root (or any even root - 4th, 6th etc) of a negative number
• The logarithm of 0 or a negative number (less common)

The expression within the square root may be negative for an extended interval, in which case the whole interval must be excluded from the domain.

Pay careful attention to the end-points: 0 within the square root is OK and can be included within the domain, unless of course the square root is also in the denominator of a fraction.