Calculus

Quote:

How do you go about solving this problem sqrt(sqrt(1+x) + 1-x)) and would you find the domain

do you mean solving for x given that sqrt(sqrt(1+x) + (1-x)) = C, where C is some number?

if so

sqrt(sqrt(1+x) + (1-x)) = C

sqrt(1+x) + (1-x) = c ²

sqrt(1+x) = (x-1) + c ²

1+x = ((x-1) + c ²) ² = (x-1) ² + 2c ²(x-1) + c ⁴

now you can collect all the terms together and end up with a quadratic expression in x which you can solve using the quadratic formula.

As far as the domain is concerned none of the terms under radicals can be negative. So

(1+x) >= 0 ---> x >= -1

(sqrt(1+x) + (1-x)) >= 0

sqrt(1+x) >= (x-1)

1+x >= (x-1) ²

and this is also a quadratic expression that can be solved using basic methods.