If `f(3x+2)+f(3x+29)=0x in R ,` then the period of `f(x)` is (a) 7 (b) 8 (c) 10 (d) none of these

If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is (a) 1 (b) 2 (c) 3 (d) 4

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

If f(x)=|sinx-|cosx||, then the value of f^'(x) at x=(7pi)/6 is (a) positive (b) (1-sqrt(3))/2 (c) 0 (d) none of these

If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 is 2 (b) 8 (c) 16 (d) 4

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

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

The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes the greatest integer function is: (a)3 (b) 2 pi (c) 2 (d) none of these

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=0 ,then f(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_e 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these