What is the domain and range of #f(x)= 1/x#?

Answer 1

Domain: #(-oo, 0) uu (0, + oo)#
Range: #(-oo, 0) uu (0, + oo)#

Your function is defined for any value of #x# except the value that will make the denominator equal to zero.

More specifically, your function #1/x# will be undefined for #x = 0#, which means that its domain will be #RR-{0}#, or #(-oo, 0) uu (0, + oo)#.

It's also crucial to keep in mind that a fraction can only equal zero if the numerator also equals zero.

Since the numerator is constant, your fraction has no way of ever being equal to zero, regardless of the value #x# takes. This means that the range of the function will be #RR - {0}#, or #(-oo, 0) uu (0, + oo)#.

graph{1/x [-3.51, 3.51, 7.025, -7.02,]}

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Answer 2

Kennedy Adams

The domain of ( f(x) = \frac{1}{x} ) is all real numbers except ( x = 0 ), and the range is also all real numbers except ( y = 0 ).

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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.