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Math·Advanced Math·Nonlinear functions

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The function $f$ is defined by $f(x)=a^x+b,$ where $a$ and $b$ are constants and $a>0$. In the $xy$-plane, the graph of $y=f(x)$ has a $y$-intercept at $(0,-20)$ and passes through the point $(2,43)$. What is the value of $a+b$?

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