Question

Consider the real-valued function given by the following rule. What is the largest domain on which this rule makes sense?

Answer 1

\[f(x) = \sqrt[4]{4-x^4}\]

Answer 2

The term under the root must be greater than or equal to zero

Answer 3

\[4-x^4 = -(x^2 +2)(x^2-2)\]

Answer 4

Or you can just say
\[4 - x^4 \ge0 ~~~so~~~~x^4 \le 4\]
\[x \le 4^{1/4}\]
\[x \le \sqrt{2}\]

Answer 5

+ or - square root of 2

so x has to be in between + and - square root 2

Answer 6

\[-\sqrt{2}\le x \le \sqrt{2}\]