give the domain....?

Question

x^2-7x+10

Answer 1

Hello Darling ;

As friends said , The domain of this function is the set of all real numbers
Domain = ( -∞ , +∞ ) OR { -∞ ≤ x ≤ +∞ }

Good Luck sweetheart ♣

Answer 2

x² - 7x + 10

As there is no restriction on what you can input into this relation its domain is all x

However
x² - 7x + 10
= x² - 2.(7/2)x + (7/2)² - 9/4 as 49/4 - 9/4 = 10
= (x - 7/2)² - 9/4

So its output has some interesting implications:
since the least possible value of a square number is zero (in the real number field anyway) then the lowest possible output of this relation is -9/4 (and that occurs when x = 7/2)

So its range is all y ≥ -9/4

If you were graphing y = x² - 7x + 10 you would get a parabola with its vertex at (7/2, -9/4) (ie (3.5, -2.25)

Answer 3

The domain is the set of al real numbers.

Answer 4

The domain is the set of numbers you can use for x.
The range is the set of numbers that will result when you calculate y.

In your example, all real numbers will work for x. So the domain is all real numbers.

Answer 5

It is a polynomial and by definition, polynomials are continuous over the set of real numbers and thus all real numbers is part of the domain.