What is the domain and range of #g(x)= 2/ (x-1)#?

1 Answer
Stefan V.
Aug 11, 2015

Domain: #(-oo, 1) uu (1, +oo)#
Range: #(-oo, 0) uu (0, + oo)#

Explanation:

The domain of the function will be restricted by the fact that the denominator cannot be equal to zero.

#x-1!=0 implies x!=1#

The domain will thus be #RR-{1}#, or #(-oo, 1) uu (1, +oo)#.

The range of the function will be restricted by the fact that this expression cannot be equal to zero, since the numerator is a constant.

The range of the function will thus be #RR-{0}#, or #(-oo, 0) uu (0, + oo)#.

graph{2/(x-1) [-7.9, 7.9, -3.95, 3.95]}

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