Question 3: Given a function y=f(x) that has derivatives and is continuous on the set of real numbers R. Know the graph of the function y=f′(x) as shown below. In which of the following ranges does the function \(y=f(6–2x)\) be inverse?

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

\(f'(x)<0\Leftrightarrow\left[\begin{array}{l}x<-2\\0

Consider the function \(y=f(6-2x)\Rightarrow y’=-2f'(6-2x)\).

For the function to be inverse, then

\(\begin{array}{l} y’ < 0 \Leftrightarrow f'(6 - 2x) > 0\\ \Leftrightarrow \left[\begin{array}{l}-2<6-2x<0\\6-2x>2\end{array}\right\Leftrightarrow\left[\begin{array}{l}3

===============