Question

(1)/(x^2-5) find the domain

Answer 1

The domain of
`f(x) = x^(2) - 5` is all real numbers, and the range is all real numbers greater than or equal to -5. The quadratic nature of the function ensures that it covers a wide range of values, and the shift downwards by 5 units does not affect the non-negativity of the output.

To find the domain and range of the function
`f(x) = x^(2) - 5` , we need to consider the possible values of x and the corresponding values of f(x).

Domain:

The domain of a function is the set of all possible input values. For a polynomial function like
`f(x) = x^(2) - 5`, there are no restrictions on the values of x. In other words, x can take any real number. Therefore, the domain is all real numbers, often denoted as (−∞,∞).

Range:

The range of a function is the set of all possible output values. For the given function
`f(x) = x^(2) - 5` , we can analyze the behavior of the quadratic function. The term
`x^(2)` implies that the function will always produce non-negative values, as the square of any real number is non-negative. By subtracting 5, the function shifts downwards by 5 units, but it still includes all non-negative real numbers. Therefore, the range is all real numbers greater than or equal to -5, often expressed as [−5,∞).

Complete question

Find the Domain and Range of
`f(x) = x^(2) - 5`.