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Chapter 1: Problem 29

Determine the domain of the function represented by the given equation. $$f(x)=x^{2}+2$$

Short Answer

Expert verified
The domain of the function \(f(x) = x^2 + 2\) is all real numbers, or in interval notation, \((-\infty, \infty)\).

Step by step solution

01

Identify the Type of Function

The given function \(f(x) = x^2 + 2\) is a quadratic function which is a type of polynomial function. There are no roots, logarithms, divisions, or other operations that might restrict the domain in this function.
02

Determine Restrictions on the Domain

In the case of this function, any real number can be squared, and adding 2 to a real number still results in a real number. Therefore, there are no restrictions to the domain because squaring has no restrictions and additions or subtractions do not affect the domain.
03

Specify the Domain

Based on the previous steps, since there are no restrictions, the domain of this function is all real numbers. In interval notation, this can be written as \((-\infty, \infty)\).

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