Question

find the domain of the function p(x) = x2 - 2x + 8
what is the dmain of p?

Answer 1

all reals

Answer 2

Ok first you want to know that is a domain of a function. A simple definition of a domain is all the values of x for which plugged in the function the values that emerge exist. For example if I have the function\[f(x) =\sqrt{x}\] then if I choose \[x = -2\] and plug it in the function then I will have\[f(-2) = \sqrt{-2}\] which clearly doesn't exist. Therefore the DOMAIN of this function is all the positive numbers, or in mathematical terms:\[D_{f(x)} = \left\{ x \ge 0 \right\}\]. Now in your case, if I have the function\[p(x) = x ^{2}-2x+8\] no matter what value I choose for x, I will always have a perfectly right answer, ex:\[p(-2) = (-2)^{2}-2(-2)+8 = 4+4+8=16\] Therefore \[D_{p(x)} = \mathbb{R}\]. Peace, Love and Happiness from Puerto Rico