Question

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

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

Short answer

The value of$f\left(g\left(2\right)\right)$ is $4$.

Step-by-step solution

– Composition of functions.

Composition of functions is defined as:

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

– Given information.

The given graph is:

– Find the required value.

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

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

The value of$f\left(g\left(2\right)\right)$ is $4$.