Show that f (x) = cx+d is a continuous function. | question and answer !

sol - The domain of linear function f(x) = cx+d is R; and let 'a' be any arbitrary real number.


lim f(x) = lim f(a+h)
x→a         h→0


= lim[c (a+h)+d]
   h→a


= ca+d                   .....(1)


f (x) = ca+d                  .....(11)


From (1) and (11),     lim f(x) = f(a)
                                   x→a


therefore  f(x) is continuous at x=a


and since a is any arbitary.        f(x) is a continuous function.