Answer
The values of the function at the given points are $g\left( 1 \right)=-2$ , $f\left( g\left( 1 \right) \right)=10$
Work Step by Step
Substitute the value of $x=1$ in $g\left( x \right)$ to get $g\left( 1 \right)$ as follows
$\begin{align}
& g\left( x \right)=3x-5 \\
& g\left( 1 \right)=3\cdot 1-5 \\
& =3-5 \\
& =-2
\end{align}$
Calculate the value of $f\left( g\left( 1 \right) \right)$ by putting the value $x=g\left( 1 \right)$ in the function $f\left( x \right)$ as follows
$\begin{align}
& f\left( x \right)={{x}^{2}}-x+4 \\
& f\left( g\left( 1 \right) \right)={{\left( -2 \right)}^{2}}-\left( -2 \right)+4 \\
& =4+2+4 \\
& =10
\end{align}$
Thus, the values of the functions at the given points $g\left( 1 \right)$ and $f\left( g\left( 1 \right) \right)$ are $-2$ and $10$ , respectively.
