Define g(x)= cases x, & 0 x< 2 1, & x= 2 x, & 2 <x cases Does there exist a value in…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Define

g(x)=\begin{cases} \sin x, & 0\le x<\tfrac{\pi}{2}\\ 1, & x=\tfrac{\pi}{2}\\ \cos x, & \tfrac{\pi}{2}<x\le \pi \end{cases}

Does there exist a value

c

[0,\pi]

for which

g(c)=0.8

? Answer "yes" or "no" and name an interval on which your conclusion is guaranteed.