Question

List all the values of x where the given function is discontinuous. In each case say why and specify the type of discontinuity

Answer 1

Given:-

A set of functions.

To find:-

Where x is discontinous.

Discontinous is defined as a lack of continuity.

Considor the function,

`f(x)=3x^2-6x+3`

The discontinuty is there when the denominater becomes zero.

Here there is no denominator. So the function is fully continous.

Considor the function,

`f(x)=x^5-x^3`

Here also there is no denominator, so the function is fully continous.

Considor the function,

`f(x)=(x+1)/(x-2)`

Here there is denominator.

For the value x is 2, the denominator will become zero.

`\begin{gathered} f(x)=(2+1)/(2-2) \\ f(x)=(3)/(0) \end{gathered}`

So the function is discontionus at x is 2.

Considor the function,

`f(x)=(3x-1)/(2x-6)`

The denominator will become zero for the value x is 3.

`\begin{gathered} f(3)=(3(3)-1)/(2(3)-6) \\ f(3)=(8)/(0) \end{gathered}`

So the function is discontinous at x at 3.