One-to-one question

Question

Explain why the following statement must be True, or provide a counterexample to show that it can be False.

If  𝑓 and  𝑔 are one-to-one functions defined on all of  ℝ, then the function  ℎ(𝑥)=𝑓(𝑥)+𝑔(𝑥) is also one-to-one

Answer 1

False

Let f(x) = x and g(x) = -x on the reals

Each is clearly 1-1.

Then, h(x) = f(x) + g(x) = x + -x = 0 is not 1-1