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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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