1. If the positive integer $a$ makes the maximum value of the function $f(x)=x+\sqrt{13-2 a x}$ also a positive integer, then this maximum value equals
1. 7 Detailed Explanation: $f(x)=y,(y-x)^{2}=13-2 a x$, then $x^{2}-(2 y-2 a) x+y^{2}-13=0, \Delta_{x} \geqslant 0 \Rightarrow 2 y \leqslant a+\frac{13}{a}$ $\in \mathbf{Z}^{+} \Rightarrow a=1, y_{\max }=7$.