Question

Find the values of x graphically which satisfy;

Function.

Solution

Correct option is

Thus to find the points for which (x) = x2 – 5 is less than or equal to g(x) = [x] and g(x) = [x] is less than or equal to h(x) = x2 – 2.

Where the three functions (x), g(x) and h(x) could be plotted as;

Thus from the above graph; x2 – 5 ≤ [x] ≤ x2 – 2 

   

where A and D is point of intersection of x2 – 5 = ± 2 ⇒

 and C is point of intersection of x2 – 2 = 1   

  

                         

SIMILAR QUESTIONS

Q1

The number of real solution of the equation

            

Q2

Number of solution of  is equal to:

Q3

Number of roots of 

Q4
Q5

The number of solution of the equation

               

where [.] denotes the greatest integer function is:

Q6

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

Q7

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

Q8

Find the values of x graphically which satisfy 

Q9

 

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

 

Q10

Find the number of solutions of  when