# What is a function that satisfies the following conditions?

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?

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