### Home > A2C > Chapter 7 > Lesson 7.3.1 > Problem7-163

7-163.

Consider the function$f ( x ) = \sqrt { x + 3 }$.

1. What are the domain and range of $f\left(x\right)$?

Think about what the graph would look like.
Try making a table if you do not remember what the graph looks like.

2. If $g\left(x\right) = x − 10$, what is $f\left(g\left(x\right)\right)$?

f(g(x)) is the same as $f\left(x − 10\right)$. Why?
Find $f\left(x − 10\right)$.

3. What are the domain and range of $f\left(g\left(x\right)\right)$?

See the hint in part (a).

4. Is $f\left(g\left(x\right)\right) = g\left(f\left(x\right)\right)$? Justify why or why not.

$f\left(g\left(x\right)\right)$ is the same as $f\left(x − 10\right)$.

$g(f(x)) \text{ is the same as } g\left(\sqrt{(x + 3)}\right).$

Will these yield the same function?