If `f(x+1/2)+f(x-1/2)=f(x) for all x in R ,` then the period of `f(x)` is 1 (b) 2 (c) 3 (d) 4

The function f: R-R is defined by f(x)=cos^2x+sin^4xforx in Rdot Then the range of f(x) is (3/4,1] (b) [3/4,1) (c) [3/4,1] (d) (3/4,1)

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a) e^2-1 (b) e^4-1 (c) e-1 (d) e^4

If f is a function such that f(0)=2,f(1)=3,a n df(x+2)=2f(x)-f(x+1) for every real x , then f(5) is 7 (b) 13 (c) 1 (d) 5

If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is x in R-{0} b. {x|x>>0} c. x in R-{0,2} d. x in R

IF f(x) = ( x+2)/(3x-1) , then f(f(x)) is

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

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

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

If f(x^2-6x+6)+f(x^2-4x+4)=2x AA in x in R then f(-3) + f(9) -5f(1)= (A) 7 (B) 8 (C) 9 (D) 10

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x , then prove that f(x) is periodic and find its period.