How do you find the domain and range of #f(x)= 2x^2-1#?

1 Answer
Aug 14, 2015

Answer:

Domain: #(-oo, +oo)#
Range: #[-1, +oo)#

Explanation:

Your function is defined for any value of #x#, so you have no restrictions wehn it comes to its domain, which will be #x in RR#, or #(-oo, +oo)#.

In order to determine the function's range, focus on the fact that you're dealing with the square of a value #x#. As you know, for real numbers, the square of any number will be positive.

This means that the minimum value this function can take will occur at #x=0#

#f(0) = 2 * 0^2 - 1 = -1#

For any value of #x !=0#, #f(x)>f(0)#. This means that the function's range will be #[-1, +oo)#.

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