Try the fastest way to create flashcards
Question

# In Exercise given below, use f(x) and g(x) to find each composition. Identify its domain. Do not use a calculator. (a) $(f \circ g)(x) \quad$ (b) $(g \circ f)(x) \quad$ (c) $(f \circ f)(x)$$f(x)=5, \quad g(x)=x$

Solution

Verified
Step 1
1 of 3

Using the given value of $f(x)$ and $g(x)$, we will determine the value of the given functions.

$\textbf{Part (a),}$

Knowing that:

$(f\cdot g)(x)=f(g(x))$

By definition:

\begin{aligned} (f\cdot g)(x)&=f(x)\\ &\boxed{=5} \end{aligned}

Function $(f\cdot g)(x)=5$ is defined for all real numbers. Therefore, its domain is $(-\infin,\infin)$.

## Recommended textbook solutions #### Precalculus

2nd EditionISBN: 9780076602186 (1 more)Carter, Cuevas, Day, Malloy
8,886 solutions #### Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions #### A Graphical Approach to Precalculus with Limits: A Unit Circle Approach

5th EditionISBN: 9780321644732 (3 more)Gary K. Rockswold, John Hornsby, Margaret L. Lial
8,829 solutions #### Precalculus with Limits

3rd EditionISBN: 9781133962885 (2 more)Larson
11,244 solutions