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

1 Answer
1s2s2p
Mar 11, 2018

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

Explanation:

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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