Explain the terms domain and range and explain how restrictions to these ?

Question

Explain the terms domain and range and explain how restrictions to these ?

Answer 1

The domain determines the range, that is, the domain is independent over its defined values while the range is dependent on the domain for its values. Take f(x) = 2x. x can be any value it wants as it is independent. If we choose 4 for x, then f(x) becomes f(4) and equals 2*4 = 8. 8 is one of the values in the range and it was dependent on our choice for x. We choose a value for x and then f(x) is computed from the value for x we choose. The values for x are its domain. The computed values for f(x) make its range and the values are dependent on the values for the domain.