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The complete graph of $y=f(x),$ which consists of five line segments, is shown in red below. (On this graph, the distance between grid lines is $1.$) Let $a$ and $b$ be the largest negative integer and the smallest positive integer, respectively, such that the functions $g(x)=f(x)+ax$ and $h(x)=f(x)+bx$ are invertible. What is $a^2+b^2?$

 

 Oct 2, 2020
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a^2 + b^2 = (-2)^2 + 3^2 = 13.

 Oct 2, 2020

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