Need some help for proving functions

[jolly geode]

I understand some of the concept but I am having trouble putting down mathematical sentences that look presentable. Help would be appreciated, thanks!

First question:

Let f : R∗ → R with f (x) = e^x + x, where R∗ is the set of all real numbers
different from 0.
i. Determine whether or not f is a one to one function.
ii. Determine whether or not f is an onto function.

Second one:

Let f : A → B and g : B → C be functions. Prove that if f and g are both
one-to-one, then g ◦ f is also one-to-one.

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[floral rapids]

By ex + x, did you mean e^x + x?
If so, you can start by analyzing the monotonicity of f(x).

[jolly geode]

Yes! I missed that out, sorry
Edited now

[jolly geode]

Can I do it like that? I'm skeptical about my workings haha

[floral rapids]

No, that's not correct.

[ripe wharf]

You assumed x_1 = x_2 in line 5.

[cerulean coral]

@jolly geode

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