An expression is well-defined if you can compute its value without any illegal operations. Examples of expressions that are not well-defined include 1/0 and sqrt-10. For what values of x is the expression

\(\frac{\sqrt{x+1}+ \sqrt{1-x}}{\sqrt{x}}\)

well defined?

Guest Apr 16, 2017

#1**+2 **

( sqrt [x + 1] + sqrt [ 1 - x]) / sqrt [x] we can write

sqrt [x + 1] / sqrt [x] + sqrt [ 1 - x ] / sqrt [x]

The domain of the first is (0, infinity) while the domain of the second is (0, 1]

The intersection of these domains is (0,1] so this interval is where the function is defined

See the graph, here : https://www.desmos.com/calculator/dea2cd3jnp

CPhill
Apr 16, 2017