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Question 783955: x^2-14x+49/100x
I have to find the domain for this problem. write the domain in set notation and find out if this expression has an excluded value or not and explain why.
I can factor the top portion to (x-7)(x-7) but then i get confused on what to do next. I haven't taken an algebra course in years and am feeling a little overwhelmed just looking at this problem.
Thank you for any help you can give me.
Faith Rayborn
faithdrayborn1@hotmail.com
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The domain of a function is the set of real numbers for which the function is defined. For polynomial functions, that is always the entire set of real numbers. For rational functions, such as your example, it is the set of real numbers with any values that would cause the denominator polynomial to equal zero excluded. For functions including radicals with an even index (square root, 4th root, 6th root, and so on), the domain is restricted to those values that make the radicand non-negative (that is to say, greater than or equal to zero).
The procedure for a radical function such as your example is to take the denominator expression, set it equal to zero, then solve for all real roots. Then the domain is the set of all real numbers except for those real zeros you found for the denominator.
Specifically, in this case:
\ =\ \frac{x^2\ -\ 14x\ +\ 49}{100x})
So set the denominator equal to zero:
And solve:
Hence  is excluded.
\ =\ \left\{x\ \in\ \mathbb{R}\ |\ x\ \not =\ 0\right\})
Read: "The domain of f is the set of all numbers  contained in the real numbers such that is not equal to zero."
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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