Give an example of a function, f(x), with a domain of (0,5] and a range of [0,∞).

Solution:

The domain is the set of all the input values a function takes and the range is the set of all the output values of the function.

An example of a function with domain (0,5] and range [0,∞) is given as

f(x) = x/|x - 5|

The numerator is x which can take the value from 0 to 5. The denominator restricts the domain value to 5 because x - 5 will be zero at x = 5.

At x = 0 f(x) = 0

At x = 5 f(x) = ∞

Give an example of a function, f(x), with a domain of (0,5] and a range of [0,∞).

Summary:

The function which has a domain of (0,5] and range of [0,∞) is f(x) = x/I x - 5 I