Use the table to evaluate the expression (f{\circ}g)(3)

Question:

Use the table to evaluate the expression

{eq}(f{\circ}g)(3) {/eq}

{eq}\begin{array}{|l|l|l|l|l|l|l|} \hline x & 1 & 2 & 3 & 4 & 5 & 6\\ \hline f(x) & 3 & 2 & 1 & 0 & 1 & 2\\ \hline g(x) & 6 & 5 & 2 & 3 & 4 & 6\\ \hline \end{array} {/eq}

Composition of Functions

If we have a function written in the form {eq}(f \circ g)(x) {/eq}, it means we have a composition of functions. We can think of this as {eq}f(g(x)) {/eq}. Thus, the output of {eq}g(x) {/eq} is the input of {eq}f(x) {/eq}.

The expression {eq}(f{\circ}g)(3) {/eq} can also be written as {eq}f(g(3)) {/eq}. In order to evaluate this, we need to first find the value of {eq}g(3) {/eq}. Then, we can evaluate f at that value.

{eq}g(3) = 2\\ f(g(3)) = f(2)\\ f(2) = 2\\ {/eq}

Thus, {eq}(f{\circ}g)(3) = 2 {/eq}.