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Stitz-Zeager_College_Algebra_e-book

# since odd roots of real numbers even negative real

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Unformatted text preview: 2 = −x2 + 3x + 6 Once again, we see there is a dramatic diﬀerence between modifying the input and modifying the output. Finally, in f (x) + f (2) we are adding the value f (2) to the expression f (x). From our work above, we see f (2) = 6 so that f (x) + f (2) = −x2 + 3x + 4 + 6 = −x2 + 3x + 10 Notice that f (x + 2), f (x) + 2 and f (x) + f (2) are three diﬀerent expressions. Even though function notation uses parentheses, as does multiplication, there is no general ‘distributive property’ of function notation. 2x . Substitution gives −9 2(3) 6 r(3) = =, (3)2 − 9 0 Suppose we wish to ﬁnd r(3) for r(x) = x2 which is undeﬁned. The number 3 is not an allowable input to the function r; in other words, 3 is not in the domain of r. Which other real numbers are forbidden in this formula? We think back to arithmetic. The reason r(3) is undeﬁned is because substitution results in a division by 0. To determine which other numbers result in such a transgression, we set the denominator equal to 0 and solve x2 − 9 x2 √ x2 x = = = = 0 9 √ 9 extract square r...
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