Question 39: Let the function y = f(x) be determined on R and have a graph as shown below. Find all real values of parameter m so that the equation 2|f(x)| – m = 0 has exactly four distinct solutions.

+ First from the graph of the function y = f( x), we deduce the graph of the function y = |f(x)| as shown below:

Equation 2|f(x)| – m = 0 or |f(x)| = m/2 is the coordinate equation of intersection of the graph of the function y = |f(x) and the line y = \(\frac{m}{2}\).

Based on the graph of the function y = |f(x)|, we have ycbt becoming:

\(0 < \frac{m}{2} < 4 \Leftrightarrow 0 < m < 8\)

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