Question
Determine the Domain of the given function
k(x) = 6x ^ 2 + 12x + 5
All real numbers
- 1 <= y <= 3
- 1 <= x <= 5
○ - 1 <= x <= 3
k(x) = 6x ^ 2 + 12x + 5
All real numbers
- 1 <= y <= 3
- 1 <= x <= 5
○ - 1 <= x <= 3
Answers
GPT-4o mini
To determine the domain of the function \( k(x) = 6x^2 + 12x + 5 \), we need to identify for which values of \( x \) the function is defined.
The function \( k(x) \) is a polynomial, and polynomial functions are defined for all real numbers, meaning there are no restrictions on \( x \) such as division by zero or square roots of negative numbers.
Therefore, the domain of the function \( k(x) = 6x^2 + 12x + 5 \) is:
\[
\text{All real numbers} \quad (-\infty, \infty)
\]
Among the options you've provided, the best choice is:
- All real numbers
The function \( k(x) \) is a polynomial, and polynomial functions are defined for all real numbers, meaning there are no restrictions on \( x \) such as division by zero or square roots of negative numbers.
Therefore, the domain of the function \( k(x) = 6x^2 + 12x + 5 \) is:
\[
\text{All real numbers} \quad (-\infty, \infty)
\]
Among the options you've provided, the best choice is:
- All real numbers