CPM Homework Help : PC Problem 1-53

In the previous problem we had $h(x)=\sqrt{x+2}$ . What is the domain of $h\left(x\right)$ ? On your calculator enter $Y1=2((\sqrt{(X+2)})^2-1)+5$ and graph the function. This is equivalent to $f\left(g\left(h\left(x\right)\right)\right)$ . Is your graph what you expected? Why do you think this occurred?

Calculator OK

Answer:

The graph does not give a full line. The line starts at $\left(−2,3\right)$ and then follows the line $y = 2x + 7$ .
Since $h\left(x\right)$ is defined for only values of $x ≥ −2$ , the composite function is only defined for $x ≥ −2$ .