The range of a R for which the function
`f (x) = (4a -3) (x + log _(e) 5) + 2 (a -7) cot ((x)/(2)) sin ^(2) ((x)/(2)), x ne 2 npi, n in N` has critical points, is :

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)(cot x)/(2)(sin^(2)x)/(2) does not possess critical points is (-oo,-(4)/(3)) (b) (-oo,-1)(c[1,oo)(d)(2,oo)

The range of the function f(x) = log_(3) (5+4x - x^(2)) , is

Range of the function f(x)=log_(e)sqrt(4-x^(2)) is

The range of the function f(x) = log_(cosec^2 (7pi)/3) (4^x – 2^x +1) is equal to

The range of the function f(x)=sin^(-1)(log_(2)(-x^(2)+2x+3)) is

The range of the function f(x)=log_((1)/(2))log_(5)(sqrt(2x^(2)+4x+7)) is

The range of the function f(x)=sin cos(ln((x^(2)+1)/(x^(2)+e))) is

The range of values of k for which the function f(x)=(2k-3)(x+tan2)+(k-1)(sin^(4)x+cos^(4)x) does not possess critical points is