How do you find the domain and range of #y = 1/x^2#?

Answer 1

Julia Adams

The domain is #color(red)(x≠0)#; the range is #color(red)(y>0)#.

#y = 1/x^2#

#1/0# is undefined, so #x# cannot equal #0#.

The domain is #x≠0#.

#x^2# is always positive, so the range is #y>0#.

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Answer 2

Avery Alexander

To find the domain and range of ( y = \frac{1}{x^2} ):

Domain: The domain consists of all real numbers except for ( x = 0 ) because division by zero is undefined.

So, the domain is ( (-\infty, 0) \cup (0, \infty) ).

Range: As ( x ) approaches positive or negative infinity, ( \frac{1}{x^2} ) approaches zero but never actually reaches it. Therefore, the range of ( y = \frac{1}{x^2} ) is ( (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.