Question

Is f(x)=1/x uniformly continuous on (0, 1)?

A) Yes
B) No

Answer 1

Yes, the function f(x) = 1/x is uniformly continuous on the interval (0,1).

Step-by-step explanation:

Yes, the function f(x) = 1/x is uniformly continuous on the interval (0,1).

A function is uniformly continuous if for any positive real number ε, there exists a positive real number δ such that whenever |x - y| < δ, it implies |f(x) - f(y)| < ε.

In this case, let's choose ε to be a positive real number. We can choose δ to be the minimum of 1/2 and ε/2. Then, whenever |x - y| < δ, we can show that |f(x) - f(y)| < ε.