Question

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

$\left(f\circ g\right)\left(0\right)$

Short answer

The value of$\left(f\circ g\right)\left(0\right)$ is $0$.

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 $g\left(0\right)=3$and $f\left(3\right)=0$. Use these values to find the required value.

$\begin{array}{c}\left(f\circ g\right)\left(0\right)=f\left(g\left(0\right)\right)\\ =f\left(3\right)\\ =0\end{array}$

Thus, the value of$\left(f\circ g\right)\left(0\right)$ is 0.