If `f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)=` ______ for x>20

If f(x)=x^(n),n in N and gof(x)=ng(x) then g(x) can be

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

If f_r(x),g_r(x),h_r(x),r=1,2,3 are polynomials such that f_r(a)=g_r(a)=h_r(a),r=1,2,3a n d F(x)=|[f_1(x),f_2(x),f_3(x)],[g_1(x),g_2(x),g_3(x)],[h_1(x),h_2(x),h_3(x)]| then F^(prime)(x)a tx=a is____________________

Let the function f satisfies f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) foe all x and f(0)=3 The value of f(x).f^(prime)(-x)=f(-x).f^(prime)(x) for all x, is

Suppose f(x)=e^(a x)+e^(b x),w h e r ea!=b , and that f^(primeprime)(x)-2f^(prime)(x)-15f(x)=0 for all x . Then the product a b is (a)25 (b) 9 (c) -15 (d) -9