What is the Domain of x^2 + 2?
In mathematics, the domain of a function is the set of all possible input values (x-values) for which the function is defined. This means we're looking for all the numbers we can plug into the expression x² + 2 and get a valid output.
Understanding the Expression
Let's break down the expression x² + 2:
- x²: This represents squaring the input value (x). Squaring any real number, positive or negative, always results in a non-negative value (0 or positive).
- + 2: This simply adds 2 to the result of x².
Finding the Domain
Since we can square any real number and then add 2, there are no restrictions on the input values. We can plug in any real number for x and get a valid output.
Therefore, the domain of the function x² + 2 is all real numbers.
Mathematical Notation
We can represent the domain using interval notation or set builder notation:
- Interval notation: (-∞, ∞)
- Set builder notation: {x | x ∈ ℝ}
Example
Let's try plugging in some values to illustrate:
- If x = 3, then x² + 2 = 3² + 2 = 9 + 2 = 11.
- If x = -2, then x² + 2 = (-2)² + 2 = 4 + 2 = 6.
- If x = 0, then x² + 2 = 0² + 2 = 0 + 2 = 2.
As you can see, we get a valid output for any value of x we choose.
Key Points to Remember
- The domain of a function is the set of all possible input values (x-values).
- The expression x² + 2 can be evaluated for any real number.
- There are no restrictions on the domain for x² + 2.
Conclusion
The domain of the function x² + 2 is all real numbers. This is because we can square any real number and then add 2, resulting in a valid output. This means there are no restrictions on the input values for this function.