Question

If \[g\] is continuous and \[g(x)\neq 0\], which function is continuous?

Options

• \[\frac{g(x)}{0}\]

• \[\frac{1}{g(x)}\]

• \[\frac{1}{0}\]

• \[g(x)-g(x)\] only when \[g(x)=0\]

Answer 1

The reciprocal of a continuous function, \[\frac{1}{g(x)}\], is continuous when \[g\] is continuous and non-zero. The non-zero condition is necessary because a reciprocal cannot have a zero denominator.