Problem 57 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the domain of the function. $$f(x)=5 x^{2}+2 x-1$$

Step-by-Step Solution

Answer

The domain of the function \(f(x) = 5x^{2} + 2x - 1\) is all real numbers.

Step 1: Recognize Type of Function

Identify the given function as a quadratic function. A quadratic function is a function that can be described by an equation of the form \(f(x) = ax^{2} + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a ≠ 0\).

Step 2: Domain of a Quadratic Function

Understand that the domain of a quadratic function is all real numbers. This is because there is no real number that we can square (for the \(x^{2}\) part) that will result in a number that is not real or that is undefined.

Step 3: Apply to Given Function

Therefore, the domain of the function \(f(x) = 5x^{2} + 2x - 1\) is all real numbers, as there are no restrictions on the values for x in the given function.