Question

Find the domain of the real valued function: f(x) = $\frac{\sqrt{2 + x} + \sqrt{ 2 -x}}{x}$

Answer 1

Answer:

⇒  Domain = [ - 2 , 0 ) ∪ ( 0 , 2 ]

OR

Domain =  x ≠ 0  ,  x ≥ - 2  ,  x ≤ 2

Step-by-step explanation:

Domain = The simplest definition of domain of a function is "The set of all possible inputs".

It is a set that includes all the input values that yield real outputs for the function.

According to the given function in the question,

It is not valid for the values of 'x' where

x = 0

So we have

x ≠ 0

Also

2 + x lies in Squre Root.

So   2 + x ≥ 0    ⇒    x ≥ - 2

AND

2 + x lies in Squre Root.

So   2 - x ≥ 0    ⇒    - x > - 2   ⇒  x ≤ 2

So we have

x ≠ 0  ,  x ≥ - 2  ,  x ≤ 2

Combining all these , we get

Domain = [ - 2 , 0 ) ∪ ( 0 , 2 ]