since odd roots of real numbers even negative real

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online