Question

Composition Using a Graph Use the given graphs of f and g to evaluate the expression.

$\left(g\circ f\right)\left(4\right)$

Short answer

The value of$\left(g\circ f\right)\left(4\right)$ is $5$.

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 graph is:

– Find the required value.

From the above graph it is clear that $f\left(4\right)=2$and $g\left(2\right)=5$. Use these values to find the required value.

$\begin{array}{c}\left(g\circ f\right)\left(4\right)=g\left(f\left(4\right)\right)\\ =g\left(2\right)\\ =5\end{array}$

Thus, the value of$\left(g\circ f\right)\left(4\right)$ is 5.