Question

State whether the following functions are continuous or discontinuous. if it is discontinuous, state the value of x which creates discontinuously.
a) f(x) = x sin x

b) f(x) = (x^2+x-12)/(x-3)

c) f(x) = √x + ((1)/(x-1))

d) f(x) =
{x-5 x <= 1
{7 x > 1

part d, it is only one curly bracket.

Answer 1

(a) since both x and sinx are continuous, so is x sinx
(b) division by zero is undefined, so there is a discontinuity at x=3
(c) same problem as (b)
(d) f(1) = 1-5 = -4
limit(x→1^⁺) = 7*1 = 7
since the two limits are different, f(x) is discontinuous at x=1