Question

) Let f: R → R be a contiuous function. Show that The function f(g(x)) attains a maximum, where g(x) = =\left\{\begin{array}{ll} \frac{x}{1+x} & x \geq 0 \\ 1 &

x<0 \end{array}\right. \text { The equation }\left(x-\frac{\pi}{2}\right)^{2} f(x)=3 \cos (2 x) \text { has at least two solutions in }(0, \pi) \text { if } f \text { is } decreasing with f(0) = 1.

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