Question

(Given \(f(x) = x^2 - 6x + 1\), what is the domain of \(f(x)\)?)

- a. \(x \geq 1\)
- b. \(x \leq -3\)
- c. \(x \geq -6\)
- d. All real numbers

Answer 1

`\[ \text{Domain of } f(x): x \geq 3 \]`

Therefore, the correct choice is not explicitly given among the options. If we were to choose the closest option, it would be (d) "All real numbers."

Step-by-step explanation:

The given quadratic function
`\( f(x) = x^2 - 6x + 1 \)` is a polynomial, and polynomials are defined for all real numbers. Therefore, the domain of
`\( f(x) \)` is all real numbers.

To find the domain, we look for any restrictions on x that would make the function undefined. In this case, there are no square roots, fractions, or logarithms in the function that would impose restrictions. Hence, the domain is all real numbers.

Therefore, the correct choice is not explicitly given among the options. If we were to choose the closest option, it would be (d) "All real numbers."