 Solution

A flux-limited galaxy selection samples a much larger volume for bright galaxies: in the nearby Euclidean limit $d_{\max }\propto \sqrt{L}$, hence $V_{\max }\propto L^{3/2}$, so very numerous faint dwarf galaxies are usually detectable only nearby. With a Schechter function $\varphi (L)\propto L^{{\alpha }_S}{e}^{-L/L_{\ast }}$, detected counts per logarithmic luminosity interval scale as $L^{{\alpha }_S+5/2}{e}^{-L/L_{\ast }}$ and, for ${\alpha }_S\sim -1$ to $-1.3$, peak near $L\sim (1.2\text{–}1.5)L_{\ast }$ rather than at the numerous faint end. The competition between increasing survey volume and the bright-end cutoff concentrates detected luminosities near $L_{\ast }$, with the precise width depending on the selection and survey depth.