Question

What is the domain of the function f(x) = x^2 + 1?

(a) All real numbers
(b) All non-negative real numbers
(c) All positive real numbers
(d) All real numbers except for 0

Answer 1

The domain of the function f(x) = x^2 + 1 is all real numbers, because any real number can be squared and then have 1 added to it without restrictions.

Step-by-step explanation:

The domain of the function f(x) = x^2 + 1 is all real numbers. This is because the equation involves squaring the variable x, which is defined for all real values of x since squaring any real number will yield a real number. Additionally, adding 1 to a real number still results in a real number, which means there are no restrictions on the value of x in this function.

The domain is not limited to only non-negative, positive, or all real numbers except for 0, as a real square function can accept any real number regardless of its sign.