How do I find the domain of #y=1/x#?

Answer 1

This is a rational function.

The denominator of a rational function cannot be #0#.

If the denominator is #0# then the rational function is undefined .

If we can find the value(s) that would result in the denominator becoming #0# then we could exclude those values when describing the domain of the function.

This is accomplished by setting the expression in the denominator equal to #0#.

#x=0# which would result in #f(x)=1/x=1/0-># Undefined

In this example the expression, #x#, will only be #0# when #x# is set to be #0#.

This means that the only value that the denominator , #x#, cannot assume is #0#.

The interval notation for the domain is #(-oo,0) uu (0,oo).#

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Answer 2

Benjamin Achtenberg

To find the domain of ( y = \frac{1}{x} ), you need to identify the values of ( x ) for which the function is defined. Since division by zero is undefined, the domain of ( y = \frac{1}{x} ) excludes any value of ( x ) that makes the denominator zero. Therefore, the domain of ( y = \frac{1}{x} ) is all real numbers except ( x = 0 ). In interval notation, the domain can be expressed as ( (-\infty, 0) \cup (0, \infty) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.