DETAILED SOLUTION needed :) Few are solved examples but I cant understand the sol. :)

1) If f(x) is a polynomial of degree n such that f(0) =0 , f(1/2) = 1/2 , ..... f(n) = n/(n+1), then find f(n+1).

2) Lef f: X-->Y, where 3^f(x) + 2^ -x = 4 be a one-one and onto function, then find the set of values of X and Y.     ; Getting diff answer for Y)

3) The polynomial P(x) is such that for any polynomial q(x) we have poq = qop . The p(x) is

A) even                B) odd

C) of even degree       D) of odd degree  ;(there are contradicting examples to the answer and solution is strange)

4) Evaluate lim x-->0  arc sin[ (arc cos x + arc cos x^2 )/pi]  ;Downright simple isnt it?

BUMP BUMP

F(x)=log₃(4 - 2^-x)

now domain of f(x) is  :     -2<x<infinity

and f'(x)=1/(4 - 2^-x)  * (-2^-x) * (-1 ) * (ln 2/ln 3) 

=(2^-x)*(ln₃2)/(4-2^-x)

now the denom. is always +ve and the num is always -ve......so  f'(x) is always -ve

hence the function is always  monotonic

and the range of f(X) is (-inf,log₃4)

so for it 2 b 1-1  & onto ,the range of Y shud b : (-inf,log₃4)

and the value  of X shud b : (-2,inf)

Yes I got something like that, the book definitely has given the wrong options and answer. :\

Can you try the other ones , especially the fourth one, for which the solution given in the book seems complete absurd.