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

1 Answer
Aug 26, 2017

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)