Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

Example 2. Given: $f(x)=2 x+3,|x| \leqslant 2$ , and $x \in Z$ . Find the range of the function.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

$\begin{array}{c} \text { Solve } \because|x| \leqslant 2, \text { and } x \in Z, \\ \therefore x \text { can only be }-2,-1,0,1,2 . \\ \text { Also } \because f(-2)=-1, f(-1)=1, f(0) \\ =3, f(1)=5, f(2)=7, \end{array}$
$\therefore$ the range of the function is $\{-1,1,3,5,7\}$ .

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