Property 2
Piecewise Function
\[f(x)=\begin{cases}h(x),&x\ge a\\g(x),&x
\(f(x)\) is a piecewise function. The point \(a\) is the critical point where the expression used to define the function changes.
1.
\(f(x)=\begin{cases}4,&x\ge1\\x+1,&x<1\end{cases}\)
\(f(2)+f(-3)+f(1)=?\)
2.
\(f(x)=\begin{cases}x^2+6,&x\ge-4\\x-1,&x<-4\end{cases}\)
\(2f(-1)-3f(0)+f(-5)+5=?\)
3.
\(f(x)=\begin{cases}14-x^2,&x\le2\\1-6x,&x>2\end{cases}\)
\((f\circ f)(2)=?\)
4.
\(f(x)=\begin{cases}3x+a,&x\ge0\\9+x,&x<0\end{cases}\)
\((f\circ f)(-2)=25\)
\(a=?\)
5.
\(f(x)=\begin{cases}x^2-4,&x>3\\1-2x,&x\le3\end{cases}\)
\(h(x)=\begin{cases}2x,&x>3\\-4,&x\le3\end{cases}\)
\((f+h)(3)+(f+2h)(4)=?\)
6.
\(f(x)=\begin{cases}4,&x>-2\\-6x,&x\le-2\end{cases}\)
\((f\circ f\circ f)(-3)=?\)
7.
\(f(x)=\begin{cases}\samefrac{x+4}{3},&x>7\\\samefrac x2,&x\le7\end{cases}\)
\(g(x)=\begin{cases}2x-4,&x<3\\x+7,&x\ge3\end{cases}\)
\((f\circ g)(4)-(g\circ f)(-2)=?\)