Question

Check the points where the constant function f(x) = k is continuous.

Answer 1

let c be a natural number.

f is continuous at x=c if lim f(x)=f(c)

L.H.S. = RHS =

lim f(x) f(x) = k

lim k f(c) = k

k

hence lim f(x)=f(c)

hence f is continuous at x=c.

f is continuous for x=c.

therefore, f is continuous for every natural number