53. Find the domain of the function p(x)=x^2-2x+7?

Question

Find the domain of the function p(x)=x^2-2x+10?

What is the domain of p?

a) x is a real number and x ≠ 7
b) x is a real number and x ≠ 0
c)x is a real number and x>0
d) x is a real number

Answer 1

The domain of a function, and the domain of the function p in this case, is the range of x values that apply to the function. Since we have a quadratic equation, x goes to infinite in both directions, positive and negative. Therefore x belogs to the set of all real numbers, and the domain is: "x is any real number", so (d) is correct!



Domain = set of x values which work for the function.



The domain of 1/(x-1) would not include x = 1 for example, Because when x = 1, then the denominator is zero and thus the function is not defined, this x value is therefore not valid or part of the domain!



Hope I explained the domain well enough ;)

Answer 2

The domain of a function is the set of all real numbers that make sense if you plug them into the function.



In this case, if you plug in any real number x, then it makes sense, because you can square any real number, or multiply it by 2, or add or subtract it from any other real number.



So the best answer is (d).



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Examples of functions with other domains include:



f(x) = 1 / (x - 3) has the domain "all real numbers except 3," because 3 doesn't make sense if you plug it into the function, because division by zero is undefined



g(x) = √x has the domain "all real numbers greater than or equal to 0", because you can't take the square root of a negative number (at least, not in the real numbers)



h(x) = ln (x) has the domain "all real numbers greater then 0," because the natural logarithm of 0 or a negative number is undefined (at least, in the real numbers).



If you haven't yet studied logarithms or don't really understand them, then feel free to ignore that last example.

Answer 3

Strictly conversing, the area could be defined to be particularly much something, yet i assume that your instructor is seeking subsets of the actual numbers. So for a million, the area is the entire set of actual numbers. for 2, that's R{-a million/2} (each and all the actual numbers different than for -a million/2), using fact -a million/2 for x could supply you a branch via 0. For a million, the only fee you ever get is 7, so the variety is purely the set {7}. for 2, the values will converge to 5/2 on the two facets, so the variety is R{5/2} (the actual numbers without 5/2).