How do you find the domain and range of #1/(x+1)#?

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Answer 1 · 2015-08-05T12:56:11

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

The domain of the function will have to take into account the fact that the denominator of the fraction cannot be equal to zero.

This means that any value of #x# that makes the expression #x+1=0# will be excluded from the domain.

More specifically, you have

#x+1 = 0 => x = -1#

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

The range of the function will be influenced by the fact that you don't have a value of #x# for which the function is equal to zero.

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

graph{1/(x+1) [-10, 10, -5, 5]}