SOLUTION: what is the domain of the function f(x)= x+10/x^2+2x-15

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Question 421085: what is the domain of the function f(x)= x+10/x^2+2x-15
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%28+x%2B10%29%2F%28x%5E2%2B2x-15%29

f%28x%29=%28+x%2B10%29%2F%28x%5E2%2B2x-15%29.......replace 2x with -3x%2B5x
f%28x%29=%28+x%2B10%29%2F%28x%5E2-3x%2B5x-15%29
f%28x%29=%28+x%2B10%29%2F%28%28x%5E2-3x%29%2B%285x-15%29%29
f%28x%29=%28+x%2B10%29%2F%28x%28x-3%29%2B5%28x-3%29%29

f%28x%29=%28+x%2B10%29%2F%28x%2B5%29%28x-3%29%29......%28x%2B5%29%28x-3%29 cannot be equal to zero
if %28x%2B5%29%28x-3%29=0...=>x%2B5=0 or x-3=0

=>x=-5 or x=3.......exclude both from domain
so
domain will be
(-infinity,-5) U (-5,-3) U (3,infinity)


Solved by pluggable solver: Plot a graph of any function AND its DOMAIN

Here's a graph of function %28x%2B10%29%2F%28x%2B5%29%28x-3%29%29 ((x+10)/(x+5)(x-3))).

The domain is shown on the x axis by a green horizontal line.