Question

Use the table to evaluate the expression.

$\left(g\circ f\right)\left(2\right)$

Short answer

The value of$\left(g\circ f\right)\left(2\right)$ is $6$.

Step-by-step solution

– Composition of functions.

Composition of functions is defined as:

$\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)$

– Given information.

The given table is:

– Find the required value.

From the above table it is clear that $f\left(2\right)=3$and $g\left(3\right)=6$. Use these values to find the required value.

$\begin{array}{c}\left(g\circ f\right)\left(2\right)=g\left(f\left(2\right)\right)\\ =g\left(3\right)\\ =6\end{array}$

Thus, the value of$\left(g\circ f\right)\left(2\right)$ is $6$.