Let `Y= (log(x+1) (x^2-3x+2) x^2)/((x-4)^3(x+5)(x-3)(x^2+2x+2))` then which of the following options is correct

Let f:RtoR be given by f(x)={{:(x^(5)+5x^(4)+10x^(3)+3x+1,xlt 0),(x^(2)-x+1,0 le x lt1),((2//3)x^(3)-4x^(2)+7x-(8//3),1 le x lt3),((x-2)ln(x-2)-x+(10//3),x ge 3):} Then which of the following options is/are correct?

Let f(x)={(x/tanx,;-ooltxlt0),(2,;x=0),(ln(1+2x)/x,;0ltxltoo):} and g(x)={(x+4,;-ooltxlt1),(x^2-5x+11,;1lexlt2),(x-3,;2lexltoo):} then which of the following is correct?

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?

For the equation x^((3)/(4)(log 2 x)^(2)+log 2(x)-(5)/(4))=sqrt(2) which one of the following is not true?

If (log_(x)x)(log_(3)2x)(log_(2x)y)=log_(x^(x^(2)) , then what is the value of y ?

Let fog (x) = log_(e) x and g(x) =(x^(4) -2x^(3) + 3x^(2) - 2x+2)/(2x^(2) - 2x + 1) Then , the domain of fog (x) is

(log (x^(3) + 3x^(2) + 3x + 1))/(log (x^(2) + 2x + 1)) is equal to

log(x^3+3x^2+3x+!)/log(x^2+2x+1)