### Home > PC > Chapter 1 > Lesson 1.1.4 > Problem1-53

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?

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 $x ≥ −2$.