Question

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

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

Short answer

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

Step-by-step solution

– Composition of functions.

Composition of functions is defined as:

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

– Given information.

The given graph is:

– Find the required value.

From the above graph it is clear that $g\left(-2\right)=1$and $g\left(1\right)=4$. Use these values to find the required value.

$\begin{array}{c}\left(g\circ g\right)\left(-2\right)=g\left(g\left(-2\right)\right)\\ =g\left(1\right)\\ =4\end{array}$

Thus, the value of $\left(g\circ g\right)\left(-2\right)$ is 4.