Question

 

Find the value of x graphically satisfying [x] – 1 + x2 ≥ 0; where [.] denotes the greatest integer function.

 

Solution

Correct option is

As,            nn     [x] – 1 + x2 ≥ 0

  

Thus to find the points for which (x) = x2 – 1 is greater than or equal tog(x) = –[x]

Where the two functions (x) and g(x) could be plotted as:

Thus from the above graph (x) ≥ g(x) when x Ïµ (–∞, A] ∪ [B, ∞), whereA is point of intersection of x2 – 1 and –[x] when –[x] = +2

  

                                                  

SIMILAR QUESTIONS

Q1

How many roots does the following equation possess 

Q2

The number of real solution of the equation

            

Q3

Number of solution of  is equal to:

Q4

Number of roots of 

Q5
Q6

The number of solution of the equation

               

where [.] denotes the greatest integer function is:

Q7

The graph of the function y = (x) has a unique tangent at (ea, 0) through which the graph passes then 

Q8

If point P(aa2) lies on the same side as that of (α, β) with respect to line x + 2y – 3 = 0 then    

Q9

Find the values of x graphically which satisfy 

Q10

Find the values of x graphically which satisfy;

Function.