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

Question

zarkon · Answer

all reals

anonymous · Answer

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