81. If f is continuous and g is a discontinuous function then f + g is discontinuous function.

if possible, let (f + g ) be continuous, and as f is continuous then
(f + g ) – f is a continuous function (∵  difference of two continuous function is continuous)
⇒  g is continuous, which is a contradiction
Hence (f + g ) is discontinuous.
Note : If f and g are discontinuous, then f + g ,fg need not be discontinuous.
For example

But (fg) (x) = (tan x) (cos x) = sin x, is continuous
(ii) 
but (f + g) (x) = 0, is continuous at x = 0