Question

If f : R  R, (x) is a differentiable bijective function, then which of the following is true?

Solution

Correct option is

  

Can’t be true as (x) – x > 0 and f’(x) is decreasing. Then (x) has to cut the line y = x.   

Similarly, (x) – x < 0 and f’(x) is increasing is not possible. 

Also, f (x) – x ≠ 0 ⇒ f (x) = -1(x) has no solution. 

SIMILAR QUESTIONS

Q1

 

Find the interval of increase or decrease of the 

                 

Q2

The function (x) = sin4 x + cos4 x increasing if:

Q3

 Then f decreases in the interval   

Q5

Find the interval for which (x) = x – sin x is increasing or decreasing.

Q6

   

Where a is positive constant. Find the interval in which f’ (x) is increasing.

Q7

If a < 0, and f (x) = eax + e–ax is monotonically decreasing. Find the interval to which x belongs.   

Q9

If (x) = ax3 + bx2 + cx + d where abcd are real numbers and 3b2 < c2, is an increasing cubic function and g(x) = af’ (x) + bf’’ (x) + c2, then

Q10

If (x) and (x) are two positive and increasing function, then