Let `f(x)=x+2|x+1|+2|x-1|dot` If `f(x)=k` has exactly one real solution, then the value of `k` is (a)`3` (b) ` 0` (c)` 1` (d) `2`

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| If the equation f(x) = k has two solutions, then true set of values of k is

Let h(x)=|k x+5| ,then domainof f(x) be [-5,7], the domain of f(h(x)) be [-6,1] ,and the range of h(x) be the same as the domain of f(x). Then the value of k is. (a)1 (b) 2 (c) 3 (d) 4

Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value of adot

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

Let f:""RrarrR be defined by f(x)""= {(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""1 , then a possible value of k is (1) 0 (2) -1/2 (3) -1 (4) 1

If f(x) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1