Is there an example of functions f and g with f’(x) = g’(x), ∀x, but f(x) ≠ g(x)?

Question

Also, why would this example be sufficient?

Answer 1

Well, there are infinitely many functions with the same derivative.

let g(x) = f(x) +1.

Then,

g'(x) = f'(x) +0.

There is no value of x for which g(x)=f(x).

To be specific, let

g(x) = 2x+1

and

f(x) = 2x.

g'(x) = f'(x) = 2.

Answer 2

You just need one example. So use an easy one.

f(x) = 5 does not equal g(x) = 6

f '(x) = 0 EQUALS g '(x) = 0

For all x values.

I dont understand what you mean by sufficient. All you need is one example because it only asks for one example.