Let and . Is the composite function continuous at ? Answer “yes” or “no” and justify…

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

Problem

Let

g(x)=\begin{cases}x^{2},&x\ge0\\-x,&x<0\end{cases}

and

f(u)=\sqrt{u}

. Is the composite function

h(x)=f(g(x))

continuous at

x=0

? Answer “yes” or “no” and justify in one sentence.