`g'(x) = -2f'(1 - 2x) + 2x- 1 = 0`

`<=> f'(1- 2x) = - \frac{1 - 2x}{2}` (*)

Đặt `1- 2x = t => f'(t) = - \frac{1}{2}t` (*)

Nghiệm của (*) là giao điểm với `y = - \frac{1}{2}t`

\begin{array}{|c|c|c|}\hline \text{$t$}&\text{$- 2$}&\text{$0$} &\text{$4$}\\\hline \text{$y$}&\text{1}&\text{0}&\text{- 2}\\\hline\end{array}

$\color{#FA8072}{\text{___}}$ $\color{#F28D84}{\text{___}}$ $\color{#EFAE98}{\text{___}}$ $\color{#E7C2AB}{\text{___}}$ $\color{#DFD6BF}{\text{___}}$ $\color{#D7E9D3}{\text{___}}$ $\color{#CFFDD7}{\text{___}}$ $\color{#C7FBEA}{\text{___}}$ $\color{#BFF9FE}{\text{___}}$ $\color{#B7F8F7}{\text{___}}$ $\color{#AFF6EC}{\text{___}}$ $\color{#A7F5DF}{\text{___}}$ $\color{#9FF3D2}{\text{___}}$ $\color{#97F2C5}{\text{___}}$ $\color{#8FF1B9}{\text{___}}$ $\color{#87F0AC}{\text{___}}$ $\color{#7FEFA0}{\text{___}}$ $\color{#77ED93}{\text{___}}$

(hình ảnh)

$\color{#FA8072}{\text{___}}$ $\color{#F28D84}{\text{___}}$ $\color{#EFAE98}{\text{___}}$ $\color{#E7C2AB}{\text{___}}$ $\color{#DFD6BF}{\text{___}}$ $\color{#D7E9D3}{\text{___}}$ $\color{#CFFDD7}{\text{___}}$ $\color{#C7FBEA}{\text{___}}$ $\color{#BFF9FE}{\text{___}}$ $\color{#B7F8F7}{\text{___}}$ $\color{#AFF6EC}{\text{___}}$ $\color{#A7F5DF}{\text{___}}$ $\color{#9FF3D2}{\text{___}}$ $\color{#97F2C5}{\text{___}}$ $\color{#8FF1B9}{\text{___}}$ $\color{#87F0AC}{\text{___}}$ $\color{#7FEFA0}{\text{___}}$ $\color{#77ED93}{\text{___}}$

`=> [(t = - 2),(t = 0),(t = 4):} => [(1- 2x = - 2),(1- 2x= 0),(1- 2x = 4):} <=> [(x = \frac{3}{2}),(x = \frac{1}{2}),(x = - \frac{3}{2}):}`

$\color{#FA8072}{\text{___}}$ $\color{#F88364}{\text{___}}$ $\color{#F68756}{\text{___}}$ $\color{#F48B48}{\text{___}}$ $\color{#F2903A}{\text{___}}$ $\color{#EF942C}{\text{___}}$ $\color{#EC981E}{\text{___}}$ $\color{#E99D10}{\text{___}}$ $\color{#E6A102}{\text{___}}$ $\color{#E2A5F4}{\text{___}}$ $\color{#DFA8E6}{\text{___}}$ $\color{#DBABD9}{\text{___}}$ $\color{#D7AECB}{\text{___}}$ $\color{#D3B1BE}{\text{___}}$ $\color{#CFB4B0}{\text{___}}$ $\color{#CCB7A3}{\text{___}}$ $\color{#C8BA95}{\text{___}}$ $\color{#C4BD87}{\text{___}}$

(hình ảnh)

$\color{#FA8072}{\text{___}}$ $\color{#F88364}{\text{___}}$ $\color{#F68756}{\text{___}}$ $\color{#F48B48}{\text{___}}$ $\color{#F2903A}{\text{___}}$ $\color{#EF942C}{\text{___}}$ $\color{#EC981E}{\text{___}}$ $\color{#E99D10}{\text{___}}$ $\color{#E6A102}{\text{___}}$ $\color{#E2A5F4}{\text{___}}$ $\color{#DFA8E6}{\text{___}}$ $\color{#DBABD9}{\text{___}}$ $\color{#D7AECB}{\text{___}}$ $\color{#D3B1BE}{\text{___}}$ $\color{#CFB4B0}{\text{___}}$ $\color{#CCB7A3}{\text{___}}$ $\color{#C8BA95}{\text{___}}$ $\color{#C4BD87}{\text{___}}$

Vậy hàm số nghịch biến trên các khoảng: `(- oo; - \frac{3}{2})` và `(\frac{1}{2};\frac{3}{2})`

`-> A. (1;\frac{3}{2})`

$\color{#FA8072}{\text{$\textit{$\circ$ hungnguyen4269}$}}$