How Can Absolute Value Definitions Be Used to Rewrite Expressions?

[mathdad]

The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| x^4 + 1 |

Since x^4 + 1 > 0, then the answer is simply the expression itself or x^4 + 1.

Correct?

 

[HallsofIvy]

Yes, for all real numbers, x, $$|x^4+ 1|= x^4+ 1$$.