Let `f(x) :R->R,f(x)={(2x+alpha^2,xge2),((alpha x)/2+10,x lt 2))` If `f(x)` is onto function then `alpha` belongs to
(A) `[1,4]`
(B) `[-2,3]`
(C) `[0,3]`
(D) `[2,5]`

If f:R to R is given by f(x)=x^(3)+(a+2)x^(2)+3ax+5a if f(x) is one-one function, then a belong to

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Let g(x)=|(f(x+alpha), f(x+2a), f(x+3alpha)), f(alpha), f(2alpha), f(3alpha),(f\'(alpha),(f\'(2alpha), f\'(3alpha))| , where alpha is a constant then Lt_(xrarr0(g(x))/x= (A) 0 (B) 1 (C) -1 (D) none of these

Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1) =5 alpha'(2) =7 then find the vlaue of beta'(1)-10