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Question 132237: Domain of the function
15/x^2-400
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! The domain is the value(s) that we can replace x with safely.
Your function is
15/(x^2 - 400)
Your denominator is clearly the difference of two perfect squares.
Your denominator becomes the following two factors: (x - 20) (x + 20).
We set each factor to = 0 and solve for x.
x - 20 = 0
x = 20
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x + 20 = 0
x = -20
What is the domain?
The domain will be ALL REAL NUMBERS EXCEPT x = -20 and x = 20?
WHY?
If you replace x with -20 and 20 in the original function, you get a ZERO in the denominator of your fraction. Division by ZERO is NOT allowed in the world of math.
That is the reason why x CANNOT be -20 or 20 for this function.
Final answer: The domain is ALL REAL NUMBERS EXCEPT x = -20 and x = 20?
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