Question 20: The function y = -x ⁴ + 4x ² – 2 is inverse on each of the following intervals?

\(\begin{array}{l} TXĐ:\,D =\mathbb{R} \\ y = f(x) = – {x^4} + 4{x^2} – 2\\ \Rightarrow f ‘(x) = – 4{x^3} + 8x\\ f'(x) = 0 \Leftrightarrow – 4{x^3} + 8x = 0\\ \Leftrightarrow \left[\begin{array}{l}x=0\\x=-\sqrt2\\x=\sqrt2\end{array}\right\end{array}\)

Variation table of the function

Based on the range of variation, conclude that the above inverse function \((-\sqrt2 ;0)\, \mathrm{and}\, (\sqrt2 ;+\infty)\)