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,

$f(x)=\frac{x+1}{x-2}$

Here there is denominator.

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

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

So the function is discontionus at x is 2.

Considor the function,

$f(x)=\frac{3x-1}{2x-6}$

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

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

So the function is discontinous at x at 3.