Question

find the domain of the function f(X) =X+1/x​

Answer 1

Step-by-step explanation:

Atlantis, a likely mythical island nation mentioned in Plato’s dialogues “Timaeus” and “Critias,” has been an object of fascination among western philosophers and historians for nearly 2,400 years. Plato (c.424–328 B.C.) describes it as a powerful and advanced kingdom that sank, in a night and a day, into the ocean around 9,600 B.C. The ancient Greeks were divided as to whether Plato’s story was to be taken as history or mere metaphor. Since the 19th century there has been renewed interest in linking Plato’s Atlantis to historical locations, most commonly the Greek island of Santorini, which was destroyed by a volcanic eruption around 1,600 B.C.

Answer 2

Answer:

$\boxed{\rm Domain \: of \: f(x) \: = \: x \in \: R; x≠ 0 }$

Step-by-step explanation:

$\red{\boxed{\rm Solution}}$

$\rm f(x) = x + \frac{1}{x} = \frac{x²+1}{x}$

We know that p/q is defined only when q ≠ 0

We know that domain is the all the possible inputs which gives a real defined output.

In order f(x) to be defined,

x ≠ 0 as x is in denominator and p/q is not defined when q = 0

We also know that a number, either positive or negative it's square is always positive for a real number.

According to the above concept,

x² + 1 ≥ 0

x² ≥ - 1

x ≥ √-1

We know that √-1 = i,

As √-1 is imaginary number,

Therefore,

All the possible inputs are all the reals numbers except 0.

$\boxed{\rm Domain \: of \: f(x) \: = \: x \in \: R; x≠ 0 }$