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Question 235932: find the domain of the function
p(x)=x^ - 2x +10
x^ means x squared, I hope I put that in right
thank you for your help, can wait to see the steps to this
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Note: x^2 means x squared, x^3 means x cubed, etc... the ^ is the exponent operator.
Ask yourself this question: Are there any numbers that if plugged into 'x' will result in an undefined expression? In other words, do you have to worry about division by zero? The answer is no. Or do you have to worry about taking the square root of negative numbers? Again, the answer is no. Do you have to consider functions like logs, and trig functions? Again, no.
Basically what I'm saying is that you can plug in ANY value for 'x' and get a real number as an output. So this means that the domain is the set of all real numbers. So in interval notation, the domain is )
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
The domain of a function is the set of values of the independent variable for which the function is defined. What this means is that if you have a number that you would like to substitute for  in your function \ =\ x^2\ -\ 2x\ +\ 10) and a real value for ) results, then the value you selected for IS in the domain set. On the other hand, if is not defined for that value of , then that value of IS NOT in the domain.
Examining the given function, we can see that there are no instances of the independent variable in a denominator. If that were the case, then we would have to exclude any value of the independent variable that would make any denominator equal to zero -- and hence make the entire function undefined. We also have no radicals with even-numbered indices, so we do not have the problem of trying to take the square or higher even numbered root of a negative number. There are also no logarithmic, trigonometric, or inverse trigonometric functions that might cause us to have domain restrictions.
In short, the domain of this function, namely is the set of all real numbers. This can be expressed in interval notation:
)
Or set builder notation:
In general, any polynomial equation of the form:
\ =\ a_nx^n\ +\ a_{n-1}x^{n-1}\ +\ a_{n-2}x^{n-2}\ +\ \cdots\ +\ a_0x^0)
( through  are constant coefficients) has a domain of all real numbers, )
John
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