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Math Help - Calculus

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Mohsin View Post
    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.

    3) Please post responses on the original thread.
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