Question

How do you find the domain and range of `f(x) = 3-2x^2`?

Answer 1

Domain; `x in RR`
Range; `f(x) <= 3`

Explanation:

It is straightforward when we sketch the function; graph{3-2x^2 [-10, 10, -5, 5]}

Hence `x in RR`
And we can prove that the greatest value of `f(x)` is 3, as `f(0) = 3`, and as the porabola is negative, then any other value of x is `<=3`

Hence `f(x) <=3` and `x in RR`