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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
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( 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