Let `f (x) = (x+5)/(sqrt(x^(2) +1) ) ,` then the smallest integral value of k for which `f (x) le k AA x in R `is

Let f (x) is a real valued function defined on R such that f(x) = sqrt(4+sqrt(16x^2 - 8x^3 +x^4)) . The number of integral values of 'k' for which f(x) =k has exactly 2 distinct solutions for k in [0,5] is

Let f(x) = cos(x) + cos(sqrt(3)x) AA x in R . The number of values of x for which f(x) is maximum is

Let f(x)=x^2-2a x+a-2 and g(x)=[2+sin^(- 1)((2x)/(1+x^2))]. If then set of real value 'a' for which f[g(x)] lt 0 AA x in R is (k_1,k_2), then the equation h(x)=[5k_1-3k_2] has 6 distinct soluuon where f(x)=|x-2| and h(x)=f(f(...........(f(x)))........), then find the value of 'n' ,(where [.] denotes the greatest integer function

Let f:R rarr(0,(2 pi)/(2)] defined as f(x)=cot^(-1)(x^(2)-4x+alpha) Then the smallest integral value of alpha such that,f(x) is into function is

Let f (x) =(2 |x| -1)/(x-3) Range of the values of 'k' for which f (x) = k has exactly two distinct solutions:

If f(x)=cos^(-1)(x^((3)/(2))-sqrt(1-x-x^(2)+x^(3))),AA 0 le x le 1 then the minimum value of f(x) is

Let f(1)=-2, f'(x) ge4.2 for 1le x le6 . The smallest possible value of f(6)-16 is ……..

Let f(x)=(kx)/(x+1) then the value of k such that f(x) is

Let f(x) = x^(2) - 3x + 2 be a function defined from R rarr R and |x| = {{:(x,, x ge 0),(-x ,, x le 0):} , then answer the following Value of k for which equation |f|x|| = k has six solutions

Let f(x) = " max " {3,x^(2),(1)/(x^(2))} for (1)/(2) le x le 2 . Then the value of integral int_(1//2)^(2)f(x) dx is