Question

determine where f is continuous.

f(x) = (sin^-1(1/x))/x

Answer 1

To determind where f(x) is continuous, think about where it is discontinuous. What values is x not allowed to take?

Answer 2

\[-1 \le x \le 1\]

Answer 3

understand the answer graphically ...can it be shown algebraically ?

Answer 4

Yeah you look at the functions involve. Essientially we have\[\sin^{-1} \frac{ 1 }{ x }\]
and \[\frac{ 1 }{ x }\] So from the second we get that x cannot be 0. For the first, we know that the domain is -1<=1/x<=1 or -1<=x<=1. Therefore the domain for f(x) is -1<=x<0 and 0<x<=1.

Answer 5

So basically look at what types of functions are involved, find each of their domains, and then combine them.