SOLUTION: Determine the domain and range of the function f(x)=5/x+1 -3 Need it explained step by step line by line

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Question 1139698: Determine the domain and range of the function
f(x)=5/x+1 -3
Need it explained step by step line by line

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=5%2F%28x%2B1%29+-3...i you are given this, then
the domain will exclude the value of x that makes denominator equal to zero, and it is
%28x%2B1%29=0
x=-1
so, domain is:
{ x element R: x%3C%3E-1 }
interval: (-infinity,-1) U (-1,infinity)
number line:
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range:
if denominator equal to zero, f%28x%29 is undefined => f%28x%29%3C%3E-3
which means, f+%28x+%29%3C-3 or f+%28x+%29%3E-3
interval: (-infinity,-3) U (-3,infinity)
so, the range is:
{ f%28x%29 element+R : f%28x%29%3C%3E-3 }