Question

What is the domain and range of `f(x) = 2x²-3x-1`?

Answer 1

See the solution below

Explanation:

Domain is the value of x that it can take, which in this case is infinite.
So it can be written as `x in(-oo, oo)`.

let us suppose
`y = 2x^2 -3x -1`

Range the values y can take

First we'll find the minimum value of of the function.

Note that the minimum value would be a co-ordinate i.e it will be of the form (x,y) but we'll only take the y value.

This can be found out by the formula `-D/(4a)`
where D is the discriminant.

`D = b^2-4ac`
`D = 9 + 4(2)`
`D = 17`

Therefore

`-D/(4a) = -17/(4(2))`

`-D/(4a) = -17/8`

graph{2x^2 - 3x-1 [-10, 10, -5, 5]}

therefore the range of `y = 2x^2 -3x -1` is
`y in (-17/8 , oo)`