Find the domain of the function
p(x)= x2 - 2x+7
The 2 next to the x is supposed to be an exponent.
Any old x will do, so all real x
A better question is: What is the RANGE?
that is a parabola
x^2-2x = p -7
x^2-2x+1 = p-6
(x-1)^2 = p-6
vertex at (1,6)
so p is never less than 6
so range of p is ≥9
so range of p is ≥6
What is the domain of p?
P(x) x^2 -2x+7
Your problem is of form p = p(x)
as stated x would have a domain and p, which depends on x, would have a range.
To elaborate a bit:
The domain of a function is the set of possible values of a function's independent variable. In this case the independent variable is x.
The range of a function is the set values of the dependent variable. In this case the dependent variable is p.
Since the vertex of this parabola is at (1,6) and it opens up (holds water), p can never be less than six, so I said the range of p is p ≥ 6
To find the domain of the function p(x) = x^2 - 2x + 7, we need to determine which values of x are valid inputs for the function. In this case, since there are no restrictions or limitations mentioned, we can assume that x can be any real number.
Therefore, the domain of the function p(x) = x^2 - 2x + 7 is all real numbers, or (-∞, +∞).