+0

# help

0
123
1

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
Sort:

#1
+77109
+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

### 13 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details