6.If `f(x)=x^(2)-x,` then prove that, `f(h+1)=f(-h)`.

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))

If f(x)=(x^(2)-1)/(x^(2)+1) prove that f((1)/(x))=-f(x)

If f(1+x)=x^(2)+1 , then f(2-h) is

If f(1+x)=x^(2)+1 then f(2-h) is

If f(x)= log_e(x+sqrt(1+x^2) , g(x)=log_e(1+sqrt(1+x^2 )and h(x)=f(x)-g(x) then prove h(1/x)=-h(x) .

(1) If f(x) = sqrt(x) , prove that : (f(x + h) - f(x))/(h) = (1)/(sqrt(x + h) + sqrtx) . (2) If f(x) = x^(2) , find : (f(1.1) - f(1))/(1.1 - 1) .

If y=|f(x)g(x)h(x)lmnabc|, prove that (dy)/(dx)=|f'(x)g'(x)h'(x)lmnabc|

If f(x),g(x) andh (x) are three polynomial of degree 2, then prove that f(x)g(x)h(x)f'(x)g'(xh'(x)f''(x)g''(x)h''(x)| is a constant polynomial.

f,g,h, are continuous in [0,a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5 Then prove that int_(0)^(a)f(x)g(x)h(x)dx=0