Let f(x) be defined on R such that `f(1)=2,f(2)=8 and f(u+v)=f(u)+kuv-2v^(2)` for all `u,v in R` (k is a fixed constant). Then,

Let f : R to R be such that, f(2x-1)=f(x) for all x in R . If f is continuous at x = 1 and f(1)=1 then-

Let 'f' be a real valued function defined for all x in R such that for some fixed a gt 0, f(x+a)= 1/2 + sqrt(f(x)-(f(x))^(2)) for all 'x' then the period of f(x) is

Let u and v be two functions defined on R as u(x)=2x-3 and v(x)=(3+x)/2 .Prove that u and v are inverse to each other.

If f(x) = log_e x, x > 0 , prove that : f (uvw) = f (u) + f (v) +f (w).

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

If f(x)=(u)/(v) then f'(x)=(1)/(v^(3))

If f(x)=ux+v the number of points in {(u,v);f(x)=fo(x)f or allxin R} is (a) finitely many (b) infinitely many (c) 2 (d) 4