CPM Homework Help : A2C Problem 7-163

Consider the function. Homework Help ✎
1. What are the domain and range of f(x)?
2. If g(x) = x − 10, what is f(g(x))?
3. What are the domain and range of f(g(x))?
4. Is f(g(x)) = g(f(x))? Justify why or why not.

Hint (a):

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

Hint (b):

f(g(x)) is the same as f(x − 10). Why?
Find f(x − 10).

Hint (c):

See the hint in part (a).

Hint (d):

f(g(x)) is the same as f(x − 10).

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

Will these yield the same function?