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

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

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

If f(x)=a x^7+b x^3+c x-5,a , b , c are real constants, and f(-7)=7, then the range of f(7)+17cosx is (a) [-34 ,0] (b) [0, 34] [-34 ,34] (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

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(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

Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of f(x) is 0 (b) -15 (c) 3-2pi none of these

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

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