Question 1: Given a function y=f(x) that has derivatives and is continuous on the set of real numbers \(\mathbb{R}\). Know the graph of the function y=f′(x) as shown below. Ask the function \(y=f(x^2)\) inverse in which of the following ranges?

Based on the graph of the function y=f'(x):

\(\begin{array}{l} y’ = f’\left( x \right) < 0 \Leftrightarrow \left[\begin{array}{l}x>4\\-1

Consider the function \(y = f({x^2}) \Rightarrow y’ = 2x.f'({x^2})\)

The inverse function derives:

\(y’ < 0 \Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x>0\\f'({x^2})<0\end{array}\right\\\left\{\begin{array}{l}x<0\\f'\left({{x^2}}\right)>0\end{array}\right\end{array}\right\Leftrightarrow\left[\begin{array}{l}\left\{\begin{array}{l}x>0\\\left[\begin{array}{l}-1<{x^2}<1\\{x^2}>4\end{array}\right\end{array}\right\\\left\{\begin{array}{l}x<0\\\left[\begin{array}{l}{x^2}<-1\\1<{x^2}<4\end{array}\right\end{array}\right\end{array}\right\\\\\\\\\\\\\\\\\\Leftrightarrow\left[\begin{array}{l}\left[\begin{array}{l}0

choose the EASY sentence

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