`phi(x)=f(x)*g(x)" and ``f'(x)*g'(x)=k` ,then `(2k)/(f(x)*g(x))=`

Suppose that h(x)=f(x)g(x) and F(x)=f(g(x)) where f(2)=3g(2)=5g'(2)=4f'(2)=-2 and f'(5)=11 then

"Prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

If f(x)=3x+6,g(x)=4x+k and fog(x)=gof(x) then k= . .

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))