Thank you for taking your valuable time to review my question. I am really stuck with the below questions, and below the question I have written what I have done so far (my chain of thought). If you would be able to tell me what I have done is right/wrong, and how the end answer is reached including working that'd be appreciated. (Please don't laugh at what I've done, I know some things may sound silly!, and sorry!)

1) The functions $f$ and $g$ are defined as follows: $f(x)= x^2-2x $ which is $x \in\mathbb R$
and also $g (x)= 2x + 3$ which is $x\in \mathbb R$

i) Find the set of values for which $f(x) > 15 $.

(I have NO CLUE how to approach this question, some pointers are appreciated). Is it that ANY $x$ value which fits in the equation must be larger than $15$? But wouldn't there be many sets of values?

ii) Find the range of $f$ and state with a reason whether $f$ has an inverse.

The minimum point is $(1, -1)$ therefore the range is $f(x) \ge -1$ correct? And yes it does have an inverse because the inverse is the other minimum point?

iii) Show that the equation $gf(x) = 0$ has no real solutions.

The square of no real number gives a negative integer?. so the equation has no real solutions?

Thank you so much guys! I've attempted to show my chain of thought as much as possible because I don't want it to seem that I'm getting you to 'do my homework' (which it isn't as it is actually just practise questions) :) and I have made an attempt as best as possible. With an exam coming up, I hope that doing these additional questions will help.

Thanks!