Find the Domain of the function step by step {√(4-x)+√(3+x)}÷{x^2-1}

Question

Find the Domain of the function step by step {√(4-x)+√(3+x)}÷{x^2-1}

Answer 1

f(x) = y = [sqr(4-x) + sqr(3+x)]/(x^2-1)

x^-1 is the denominator which cannot = 0

x can't be =-1 or 1, as they make the denominator = 0

x can't be greater than 4, as it makes a square root of a negative number: sqr(4-x)

x can't be less than -3, as it makes a square root of a negative number: sqr(3+x)

x cannot be x=-1, x=1, x<-3, x>4

domain is all other x values which are 3 intervals:

domain: [-3,-1)U(-1,1)U(1,4]

domain is the Union of 3 intervals, the middle interval open at both ends, the other two closed at one end and open at the other