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 (x^(2)-6x+6)+f(x^(2)-4x+4)=2x AA in x in Rf(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

If f(x)+2f(1-x)=6x(AA x in R) , then the vlaue of (3)/(4)((f(8))/(f'(1))) is equal to

If f (x) =x ^(2) -6x + 9, 0 le x le 4, then f(3) =

f(x)=2x^(3)-6x^(2)+6x+5(n in R)then f'(x)=

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

If A = {1, 2, 3, 4, 5, 6, 7, 8} then the number of onto functions f: A -> A so the f(x) != x, f(x) = even when x is even and f(x) = odd when x odd is (A) 18 (B) 9^9 (C) 81 (D) 64

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

if f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then f'(3)+f'(6)= (A) 0 (B) 1 (C) 2 (D) 1/2