Finding Discontinuous Composite Function f o g at x = 0

[Jan Hill]

Homework Statement

I need to find functions f and g both continuouis at x = 0 for which the composite f at g is discontinuous at x = 0

Homework Equations

The Attempt at a Solution

I thnk it is a matter of looking for a composite function that results in 0 being in the denominator so that it's undefined. Is that the only way to get this composite to be discontinuous?

 

[Jan Hill]

and can it be that f\circ g is discontinuous at x = 0 if f and g are both continuous at x = 0 despite the fact that we know that g\circ f cannot be discontinuous at x = 0 if f and g are continuous at x= 0