What is the domain of 1 / <msqrt> x 2 </msup> &#x2212;<!-- −

Monfredo0n

Monfredo0n

Answered question

2022-05-23

What is the domain of 1 / x 2 4 using the set builder notation?
I'm confused when it comes to getting the domain of a function using set builder notation. Please explain also how to do the system of inequalities when getting the domain of the given function
x 1 x 2 4

Answer & Explanation

Haleigh Vega

Haleigh Vega

Beginner2022-05-24Added 13 answers

You want to find the domain of 1 x 2 4 .We need two things: the denominator must be defined, and nonzero.The denominator is equal to zero when x = ± 2.We also have x 2 4 < 0 if 2 < x < 2, so the denominator is not defined for x ( 2 , 2 ).*
Therefore, the function is NOT defined on x [ 2 , 2 ], and thus the function IS defined on { x R | x < 2   or   x > 2 }
Or more simply, { x R | x | > 2 }
*Notice that x 2 4 < 0 x 2 < 4 | x | < 2, since x 2 = | x |.
Then, since | x | = 2 also makes f ( x ) undefined, we have f ( x ) is defined for reals where | x | > 2.

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