What is the domain and range of #f(x)= (x+1)/(x^2+3x-4)#?

1 Answer
Sep 21, 2015

Answer:

Domain: #RR-{4, +1}#
Range: #RR#

Explanation:

Given #f(x)=(x+1)/(x^2+3x-4)#

Notice that the denominator can be factored as
#color(white)("XXX")(x+4)(x-1)#
which implies that the denominator would be #0# if #x=-4# or #x=1#
and since division by #0# is undefined
the Domain must exclude these values.

For the Range:
Consider the graph of #f(x)#
graph{(x+1)/(x^2+3x-4) [-10, 10, -5, 5]}
It seems clear that all values of #f(x)# (even within #x in(-4,+1)#) can be generated by this relation.
Therefore the Range of #f(x)# is all Real numbers, #RR#