Question 7: Let the function y=f(x) have a derivative on \(\mathbb{R}\) and have a graph of the function y=f'(x) as shown in the figure. Set \(g(x)=f\left(x^{2}-2\right)\) Which of the following statements is false?

We have \(g^{\prime}(x)=2 xf^{\prime}\left(x^{2}-2\right)\)

\(g'(x)=2 xf^{\prime}\left(x^{2}-2\right)>0 \Leftrightarrow\)\(\left[\begin{array}{l}\left\{\begin{array}{l}x>0\\f^{\prime}\left(x^{2}-2\right)>0\end{array}\right\\\left\{\begin{array}{l}x<0\\f^{\prime}\left(x^{2}-2\right)<0\end{array}\right\end{array}\right\)\(\Leftrightarrow\left[\begin{array}{l}\left\{\begin{array}{l}x>0\\x^{2}-2>2\end{array}\right\\\left\{\begin{array}{l}x<0\\x^{2}-2<2\end{array}\right\end{array}\right\)\(\Leftrightarrow\left[\begin{array}{l}x>2\\-2

so the above covariate function \((2 ;+\infty)\) so A is correct

The function is covariate on (-2;0) so it is also covariate on (-1;0).

So C is wrong.

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