Concept Check The tables give some selected ordered pairs...

Concept Check The tables give some selected ordered pairs for functions $f$ and $g$ $$ \begin{array}{c|c|c|c} x & 3 & 4 & 6 \\ \hline f(x) & 1 & 3 & 9 \\ \end{array} $$ $$ \begin{array}{c|c|c|c|c} x & 2 & 7 & 1 & 9 \\ \hline g(x) & 3 & 6 & 9 & 12 \\ \end{array} $$ Find each of the following $$ (g \circ f)(3) $$

Concept Check The tables give some selected ordered pairs for functions $f$ and $g$
$$
\begin{array}{c|c|c|c}
x & 3 & 4 & 6 \\
\hline f(x) & 1 & 3 & 9 \\
\end{array}
$$
$$
\begin{array}{c|c|c|c|c}
x & 2 & 7 & 1 & 9 \\
\hline g(x) & 3 & 6 & 9 & 12 \\
\end{array}
$$
Find each of the following
$$
(g \circ f)(3)
$$

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Key Concepts

Function

A function is a mapping from a set of inputs to a set of outputs where each input is paired with exactly one output. Functions can be represented in many ways, including through tables, equations, or graphs, and they encapsulate the idea of a consistent rule that assigns outputs to inputs.

Composition of Functions

Function composition is the process of applying one function to the result of another function. Denoted as (g ? f)(x), it requires first evaluating the inner function f at x and then applying the outer function g to the result. This concept is central in understanding how simple functions combine to form more complex operations.

Function Evaluation

Evaluating a function involves substituting a particular input value into the function to determine the corresponding output. When functions are presented in a tabular format, this means locating the input in the table and reading the associated output, which is a fundamental skill for understanding and working with functions.

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