find the domain of following?

Question

1.cos(inverse)(1-2IxI)/3) + log(base)Ix-1I x where I I represents modulus function.
2. sqrt(sin(inverse)(3x-4x^3)) +sqrt(cos(inverse)x)
3.Find period of sin((piex)/(n-1)!)+ cos((piex)/(n!))

Answer 1

1) I suppose you meant arcos if so
-1<= 1-2IxI/3 <=1 and x not =1
1-2IxI/3<=1 always
-2<= -2IxI/3
1>=IxI/3 so domain IxI <=3 and x not =1
2) First
0<=3x-4x^3<=1 4x^3-3x+1>=0 so(x-1/2)(x+2)(x-1)>=0
so -2<=x<=1/2 and x>=1
0<=x(3-4x^2) because of the sqrt.
x<=-1/2sqrt3 and 0<=x<=1/2sqrt3ç
so for this summand -2<=x<=-1/2sqrt3 and 0<=x<=1/2
For the second -1<=x<=1
so the domain is -1<=x<= -1/2sqrt3 and 0<=x<=1/2
The period of the first summand is
2(n-1)!
and the second has period 2(n)!
so the period is 2(n!)

Answer 2

Please write your expressions using standard notation. As they stand, they are subject to too many different interpretations.