Answer
The value of\[g\left( 1 \right)=-2\ \text{and}\ f\left( g\left( 1 \right) \right)=10\].
Work Step by Step
Put\[x=1\ \text{in}\ g\left( x \right)=3x-5\ \text{to}\ \text{get}\ \text{the}\ \text{value}\ \text{of}\ g\left( 1 \right)\ \text{as}\ \text{follows:}\]
\[\begin{align}
& g\left( 1 \right)=3\left( 1 \right)-5 \\
& =3-5 \\
& =-2
\end{align}\]
Now, put \[g\left( 1 \right)=-2\ \text{in}\ f\left( x \right)={{x}^{2}}-x+4\ \text{to}\ \text{get}\ \text{the}\ \text{value}\ \text{of}\ f\left( g\left( 1 \right) \right)\ \text{as}\ \text{follows:}\]
\[\begin{align}
& f\left( g\left( 1 \right) \right)={{\left( -2 \right)}^{2}}-\left( -2 \right)+4 \\
& =4+2+4 \\
& =10
\end{align}\]
The value of\[g\left( 1 \right)=-2\ \text{and}\ f\left( g\left( 1 \right) \right)=10\].
