Solve f(x) > 0

[mathdad]

Given f(x) = x^2 - 4, solve f(x) > 0.

Solution:

I know that f(x) = x^2 - 4.
I also know that f(x) > 0 means to let the given function be greater than 0.

Replace > with the = symbol.

x^2 - 4 = 0

Factor.

(x - 2)(x + 2) = 0

x = 2, x = -2

Pick a number between 2 & -2.

Let x = 0.

x^2 - 4 > 0

(0)^2 - 4 > 0

-4 > 0...false statement.

I conclude that the solution to the given quadratic inequality is found in the following intervals:

(-infinity, -2) (2, infinity)

I hope to be right.

 

[JeffM]

Yes, the answer is right, but the method that you used works only for quadratics.

The slightly more complicated method discussed by Patrick and me in a different thread of yours works for every continuous function.

 

[mathdad]

Yes, the answer is right, but the method that you used works only for quadratics.

The slightly more complicated method discussed by Patrick and me in a different thread of yours works for every continuous function.

I just wanted to try a different method.
Solution with the union symbol is

(-infinity, -2) U (2, infinity)