Question

By definition, $\left(f\circ g\right)\left(x\right)=\_\_\_\_\_$. So if $g\left(2\right)=5$and $f\left(5\right)=12$,then$\left(f\circ g\right)\left(2\right)=\_\_\_\_\_$

Short answer

The required values are $\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$and $\left(f\circ g\right)\left(2\right)=12$

Step-by-step solution

–Composition of function.

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 values are:

$\begin{array}{c}g\left(2\right)=5\\ f\left(5\right)=12\end{array}$

– Find the required value.

According to composition of functions:

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

Substitute $x=2$in the above equation.

$\begin{array}{l}\left(f\circ g\right)\left(2\right)=f\left(g\left(2\right)\right)\\ \left(f\circ g\right)\left(2\right)=f\left(5\right)\\ \left(f\circ g\right)\left(2\right)=12\end{array}$

Thus, the required values are$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$ and$\left(f\circ g\right)\left(2\right)=12$