Answer
$f_{\text {ave }}=k$
Work Step by Step
By definition:
\[
\frac{1}{A} \iint_{R} f(x, y) d A=f_{\text {ave }}
\]
When
\[
\iint_{R} d A=A
\]
If $f(x, y)=k,$ then
\[
\begin{array}{l}
k \iint_{R} d A=\iint_{R} f(x, y) d A \\
k \cdot A=\quad \iint_{R} f(x, y) d A
\end{array}
\]
Divide both sides by $A$
\[
k=\frac{1}{A} \iint_{R} f(x, y) d A
\]
$f_{\text {ave }}=k$
