If `f(x)=3^(x)`, then prove that f(x + 1) = 9f(x - 1).

If f(x)=2^(x) , then prove that f(x +1) = 4f( x - 1).

If f(x)=4^(x) , then prove that (f(x+1))/(f(x-1))=16 .

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .

If f(x)=x-(1)/(x) then prove that f(x)=-f((1)/(x))

If f(x) = log_e ((1-x)/(1+x)) , then prove that f(x) + f(y) = f((x + y)/(1 + xy))

If f(x)=(1-x)/(1+x) , then prove that f(x)+f(1/x)=0 .

If f(x)=(1)/(1-x) , then prove that : f[f{f(x)}]=x

If f(x)=(1)/(1-x) , then prove that : f[f{f(x)}]=x

If f(x)=2x^(2)+3x-5 , then prove that f'(0)+3f'(-1)=0

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