If `f: Rrarr[0,oo)`is a function such that `f(x-1)+f(x+1)=sqrt(3)f(x),` then prove that `f(x)` is periodic and find its period.

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x , then prove that f(x) is periodic and find its period.

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

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

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find f'(x) if f(x)=sqrt(x^(2)-1)

If f : RR to RR is defined by f (x) = 2x -3, then prove that f is a bijection and find its inverse.

If f: X rarr[1,oo) is a function defined as f(x)=1+3x^3, find the superset of all the sets X such that f(x) is one-one.