Question

Consider the function g(x)=√x​. Is the function one-to-one?

A) Yes, for all real numbers x
B) Yes, but only for positive real numbers x
C) No, for all real numbers x
D) No, but only for negative real numbers x

Answer 1

No, the function g(x) = √x is not one-to-one for all real numbers x.

Step-by-step explanation:

No, the function g(x) = √x is not one-to-one for all real numbers x. A function is considered one-to-one if every element in the domain maps to a unique element in the range and vice versa. In other words, for the function to be one-to-one, no two different values of x should produce the same value of g(x). However, in the case of g(x) = √x, for example, both √4 and √16 produce the same value of 2. Therefore, the function is not one-to-one.