Question

What is the domain of the rational parent function, f(x) = 1/x, and the reciprocal of x-squared parent function, f(x) = 1/x²?

A) Domain: All real numbers
B) Domain: All real numbers except x = 0
C) Domain: All real numbers except x = 1
D) Domain: Only positive real numbers

Answer 1

The domain for both f(x) = 1/x and f(x) = 1/x² is all real numbers except x = 0, matching option B.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) that the function can accept without resulting in an undefined output. For the rational parent function f(x) = 1/x, the only value that cannot be in the domain is 0 because dividing by zero is undefined. As such, the domain of f(x) = 1/x is all real numbers except x = 0.

Similarly, for the reciprocal of x-squared function f(x) = 1/x², 0 is also excluded from the domain because 1 divided by 0² is still dividing by zero, which is undefined. Therefore, the domain for both functions is all real numbers except x = 0, which corresponds to option B.