1. ## Calculus

according to the book 'Calculus,early transcendentals' by HOWARD ANTON,IRL BIVENS,STEPHEN DAVIS THE DEFINITION OF FUNCTION IS "IF A VARIABLE Y DEPENDS ON A VARIABLE X IN SUCH WAY THAT EACH VALUE OF X DETERMINES EXACTLY ONE VALUE OF YTHEN WE SAY THAT Y IS A FUNCTION OF X".YES YHE QUE IS ON y^2 = x-1?HERE Y IS NOT A FUNCTION OF X.BECAUSE FOR EACH VALUE OF X DETERMINES 2 VALUE OF Y.BUT IN THE FUNCTION Y=√(X-1) FOR EACH VALUE OF X DETERMINES TWO VALUES OF Y.AS AN EXAMPLE IF X=10 THEN Y =3 OR Y=-3.SO HOW Y IS A FUNCTION OF X?AND IF Y IS NOT A FUNCTION OF X,HOW WE WILL DETERMINE THE DOMAIN?

2. Originally Posted by Mohsin
BUT IN THE FUNCTION Y=√(X-1) FOR EACH VALUE OF X DETERMINES TWO VALUES OF Y.AS AN EXAMPLE IF X=10 THEN Y =3 OR Y=-3.
1) This is a common misunderstanding. ONLY the positive value of 'Y' is indicated by this expression. This IS a function.

2) Your example is good for y^2 = x-1, but it should be noted that x-1 >= 0 (Since y^2 >=- 0), making x >= 1 a pretty good guess at the Domain.