How do you find the domain and range of f(x)= 2x^2-1f(x)=2x2−1?

1 Answer
Stefan V.
Aug 14, 2015

Domain: (-oo, +oo)(−∞,+∞)
Range: [-1, +oo)[−1,+∞)

Explanation:

Your function is defined for any value of xx, 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]}

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