Continuous Domain

[suicoted]

The function f(x) = [sroot(1+x)-sroot(1-x)]/x has had its domain extended by defining f(0) = k. What is the new domain, and what is f(0) if the function is to be continuous? Can someone verify my method, thanks?

So far, I know x cannot be 0, b/c defining by 0 is not allowed.
In interval notation, where U is union

(-infinity,0)U(0,+infinity)

x cannot be -1 and 1, b/c that would make the numerator 0, so new domain

(-infinity,-1)U(-1,0)U(0,1)U(1,+infinity)

If I'm right, I'm trying to figure out f(0) = k. I'm kind of unsure about that. Is it 1 or something? Taking a lucky guess. Thanks.

 

[Gene]

You are going astray with the sqrts. You can't take the sqrt(negative) so x can't be <-1 nor >1 or one of them will be negative. sqrt(0) is all right in the numerator so -1 and 1 are all right too. Your guess about k is correct too. To prove it, multiply the numerator and denominator by
sqrt(1+x)+sqrt(1-x), simplify then let x=0.