Question

Number of values of x in [1,2] the function f(x)=[x^4+1] is not continuous​

Answer 1

Given :

The given function is :

f(x) = $[x^4 + 1]$

To Find :

Number of values of x in the interval [1,2] where f(x) is not continuous = ?

Solution :

Here the given function is a greatest integer function .

We know that greatest integer function is discontinuous at integral points .

Since here , x ∈ [1,2]

⇒$x^4$ ∈ [1, $2^4$]

Or, $x^4$ ∈ [1 , 16]

Or, $x^4$ +1 ∈ [2,17]

So , the function f(x) has a range [2,17] .

Here the total no of integral points between 2 and 17 is 14 .

Hence total no of points of discontinuity of f(x) in  the interval [1,2] is 14 .