gaokao 2024 Q6

gaokao · China · national-II 5 marks Curve Sketching Number of Solutions / Roots via Curve Analysis
Let $f ( x ) = a ( x + 1 ) ^ { 2 } - 1 , g ( x ) = \cos x + 2 a x$. When $x \in ( - 1,1 )$, the curves $y = f ( x )$ and $y = g ( x )$ have exactly one intersection point. Then $a =$
A. $- 1$
B. $\frac { 1 } { 2 }$
C. 1
D. 2
Let $f ( x ) = a ( x + 1 ) ^ { 2 } - 1 , g ( x ) = \cos x + 2 a x$. When $x \in ( - 1,1 )$, the curves $y = f ( x )$ and $y = g ( x )$ have exactly one intersection point. Then $a =$\\
A. $- 1$\\
B. $\frac { 1 } { 2 }$\\
C. 1\\
D. 2