What is the domain and range of #F(x) = 5/(x-2)#?

Answer 1

#text(Domain): x!=2#
#text(Range): f(x)!=0#

The domain is the range of #x# values which give #f(x)# a value that is unique, such there is only one #y# value per #x# value.
Here, since the #x# is on the bottom of the fraction, it cannot have any value such that the whole denominator equals zero, i.e. #d(x)!=0# #d(x)=text(denominator of the fraction that is a function of)# #x#.
#x-2!=0# #x!=2#
Now, the range is the set of #y# values given for when #f(x)# is defined. To find any #y# values that cannot be reached, i.e. holes, asymptotes, etc. We rearrange to make #x# the subject.
#y=5/(x-2)#
#x=5/y+2#, #y!=0# since this would be undefined, and so there are no values of #x# where #f(x)=0#. Therefore the range is #f(x)!=0#.
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Answer 2

The domain of ( F(x) = \frac{5}{x-2} ) is all real numbers except ( x = 2 ), since the function is undefined at ( x = 2 ) due to division by zero. The range is all real numbers except ( y = 0 ), since the function will never reach ( y = 0 ) as ( x ) approaches infinity or negative infinity.

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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.

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.

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.

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.

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