Question

find the domain of the function.\\(f(x) = 5x^2 + 3x - 1\\)\
select one:\
a. \\((0, \infty)\\)\
b. \\((-\infty, \infty)\\)\
c. \\((-\infty, 0) \cup (0, \infty)\\)\
d. \\((-\infty, 0)\\)

Explanation:

Step1: Identify the function type

The function \( f(x) = 5x^2 + 3x - 1 \) is a polynomial function (specifically a quadratic function, since the highest power of \( x \) is 2).

Step2: Recall the domain of polynomial functions

Polynomial functions (including linear, quadratic, cubic, etc.) are defined for all real numbers. This is because there are no restrictions such as division by zero (which would occur in rational functions) or taking square roots of negative numbers (which would occur in square - root functions) for any real value of \( x \) in a polynomial. So, for \( f(x)=5x^{2}+3x - 1 \), \( x \) can take any real value, which means the domain is all real numbers, or in interval notation, \( (-\infty,\infty) \).

Answer:

B. \((-\infty, \infty)\)