Please show as much work as possible Thanks Let loga are 2r

Please show as much work as possible, Thanks!

Let loga (are 2r 1) f(z) Find the domain of f and write your answer in interval notation.

Solution

f(x) = log2(x^2 +2x +1)/(x-1)^1/3

denominator should not be zero: x<1 or x>1

log2(x^2 +2x +1) : x^2 +2x +1 >0

(x +1)^2 >0

x+1 >0 ---> x >-1

x+1<0 ---> x < -1

So, solution from the above inequalities : x< -1 or -1<x<1 or x>1

Domain : ( -inf, -1) U ( -1, 1) U ( 1, inf)