Question

Removable and Nonremovable Discontinuities: Find x values (if any) at which f is not continuous? f(x)=3x-cosx Thank you!

Answer 1

`f` is continuous for all real values.

Explanation:

We know that `3x` is a continuous function over `RR` and it can easily be proven that `cos` is also continuous over `RR`.

There is a theorem which states that sums, differences, products and quotients of continuous functions are also continuous.

We see that `f` is the difference of two continuous functions so `f` itself is continuous.