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I need help to find a well-defined function that satisfies this:

Let $A\subset \{0, 1, . . . , 9\}$ be a set and $A_c \subset A$ the subset of all even numbers in the set $A.$ Consider a concrete function $f : [−10, 10] \to R $ of your choice with the following properties:

$f(−10) = 1 = f(10)$

$f$ is continuous everywhere except at $A_c$

$f$ is differentiable everywhere except at $A.$

I've done this but is there a different way? I've done this but is there a different way

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Consider the function defined by $$1+(x+10)(x-10)\frac{\sqrt[3]{(x-1)^2(x-3)^2(x-5)^2(x-5)^2(x-9)^2}}{x(x-2)(x-4)(x-6)(x-8)}.$$

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