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

Oct 29, 2017

Domain; $x \in \mathbb{R}$
Range; $f \left(x\right) \le 3$

#### Explanation:

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

Hence $x \in \mathbb{R}$
And we can prove that the greatest value of $f \left(x\right)$ is 3, as $f \left(0\right) = 3$, and as the porabola is negative, then any other value of x is $\le 3$

Hence $f \left(x\right) \le 3$ and $x \in \mathbb{R}$