SOLUTION: are my domains correct? √(x-5)^2: [5,inf) √(x^2-5): [5,inf) (√(25-x^2))/√(1+x): (-1,5]U[5,inf) Thanks!

Algebra ->  Functions -> SOLUTION: are my domains correct? √(x-5)^2: [5,inf) √(x^2-5): [5,inf) (√(25-x^2))/√(1+x): (-1,5]U[5,inf) Thanks!      Log On


   

Question 947497: are my domains correct?
√(x-5)^2: [5,inf)
√(x^2-5): [5,inf)
(√(25-x^2))/√(1+x): (-1,5]U[5,inf)
Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%28x-5%29%5E2%29=x-5:
domain:
{ x element R : x%3E=5 }; so, [5,inf) is correct


sqrt%28%28x%5E2-5%29%29: => means x%5E2-5 cannot be equal to zero
it will be x%5E2-5=0 if x%5E2=5=>x= ± sqrt%285%29
=>x=sqrt%285%29 or x=-sqrt%285%29
{ x element R : x%2Bsqrt%285%29%3C=0 or x%3E=sqrt%285%29}
so, domain is (-infinity,-sqrt%285%29] U [sqrt%285%29,infinity)



%28sqrt%2825-x%5E2%29%29%2Fsqrt%281%2Bx%29: (-1,5]U[5,inf)-not correct

{ x element R : -1%3Cx%3C=5 }
(-1 ,5]