Question

If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?

a. 6
b. 0
c. -6

It would be great if you could add a few words of explanation

Answer 1

`f (x) = x^2 - 3 \\ \\ a.\ 6 \\ \\f(x)=6\\ \\ 6=x^2-3\\ \\6+3= x^2`


`x^2=9 \\ \\x^2-9=0\\ \\(x-3)(x+3)=0 \\ \\x-3=0 \ \ or \ \ x+3 =0 \\ \\x=3 \ \ or \ \ x= -3 \\ \\ Answer : \ Possible .`



`b.\ \ 0 \\ \\f(x)=0\\ \\ 0=x^2-3\\ \\(x-√(3)) (x+√(3))=0 \\ \\ x-√(3)=0 \ \ or \ \x+√(3) =0`


`x=√(3) \ \ or \ \x=-√(3) \\ \\Answer : \ x \ is \ not \ an \ integer,\ not \ possible`



`c.\ \ -6 \\ \\f(x)= -6\\ \\ -6=x^2-3\\ \\ x^2=-6 +3 \\ \\x^2=-3\\ \\Answer: \ square \ of \ an \ integer \ can \ not \ be \ negative`