## Related questions with answers

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

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Using 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 $(-\infin,\infin)$.

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