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