For the function, determine all values at which the function is discontinuous.

Answer

- The function definition says

The denominator factors, therefore we could rewrite this as

This function is undefined, and therefore discontinuous, at *x* = 4 and *x* = 5.The only place limits could go wrong, besides *x* = 4 and *x* = 5, is when *x* = 1. At *x* = 1 we have

As *x* approaches 1 from the left we have

As *x* approaches 1 from the right we have

Since the one-sided limits agree,

This agrees with *h*(1) = 1,

so the function is continuous at *x* = 1.

To summarize, *h* is only discontinuous at *x* = 4 and *x* = 5.