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

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Answer 1 · 2017-08-26T13:11:04

See the solution below

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)#