`f+g` may be a continuous function, if (a) f is continuous and g is discontinuous

f + g may be continuous function, if

If f(x) be continuous function and g(x) be discontinuous, then

Let f be a continuous,g be a discontinuous function.Prove that f+g is discontinuous function.

Let f and g be two real functions;such that fog is defined.If g is continuous at x=a and f is continuous at g(a); show that fog is continuous at x=a

Let f be a continuous, g be a discontinuous function. Prove that f + g is discontinuous function.

Let f(x)=[x], where [.] is the greatest integer fraction and g(x)=sin x be two valued functions over R. Which of the following statements is correct? (a) Both f(x) and g(x) are continuous at x=0 (b) f(x) is continuous at x=0, but g(x) is not continuous at x=0. (c) g(x) is continuous at x=0, but f(x) is not continuous at x=0. (d) Both f(x) and g(x) are discontinuous at x=0

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.