Answer
The value of the given expression is\[\frac{f\left( a+h \right)-\left( a \right)}{h}=3\]
Work Step by Step
Calculate the function value for $x=a+h$ and for $x=a$
$\begin{align}
& f\left( x \right)=3x+7 \\
& f\left( a+h \right)=3\left( a+h \right)+7 \\
& f\left( a \right)=3a+7
\end{align}$
Now, substitute these values in the given expression to calculate its value
$\begin{align}
& \frac{f\left( a+h \right)-\left( a \right)}{h}=\frac{3\left( a+h \right)+7-\left( 3a+7 \right)}{h} \\
& =\frac{3a+3h+7-3a-7}{h} \\
& =\frac{3h}{h} \\
& =3
\end{align}$
Thus, the value of the expression is $\frac{f\left( a+h \right)-\left( a \right)}{h}=3$.
