State True or False for the statements
If f .g is continuous at x = a, then f and g are separately continuous at x = a.

Question

State True or False for the statements If f .g is continuous at x = a, then f and g are separately continuous at x = a.

Philoid · Accepted Answer

False

Let f(x) = x and

∴ f(x).g(x) = = 1, which is a constant function and continuous everywhere.

But, is discontinuous at x=0.

State True or False for the statementsIf f .g is continuous at x = a, then f and g are separately continuous at x = a.