f)
If g:[1,a] -> R where g(x) = f(x) and g is one-one, write down the largest possible
value of a.
This is part f) of the Q.2, which gives the function $\displaystyle -2x^2+5x-3$ for $\displaystyle x \in [1,\infty)$
I'm just a little confused over all of this. Pretend that I haven't done the problem up to this point. What the heck is f(x) anyway? Are you saying $\displaystyle f(x) = -2x^2 + 5x - 3$?
You have $\displaystyle g: [1, a] \to \mathbb{R}: g(x) = f(x)$. You know that g is one-to-one.
So the question is really: Given the restriction of the domain of f to [1, a], what is the largest value of a such that f(x) is one-to-one.
If your $\displaystyle f(x) = -2x^2 + 5x - 3$ then it looks like x = 1 is on the left of the vertex, so a would have to be the x coordinate of the vertex of f(x). (That's the accurate way to say what I think you were trying to say.)
-Dan