= Solution
In a <generalized linear model>, the <linear predictor> is $\eta_i=x_i^T\beta$, a linear combination of the covariates with unknown coefficients. The <link function> relates this predictor to the <mean>: $g(\mu_i)=\eta_i$. The <canonical link function> chooses the natural parameter of the <exponential family>, namely $g(\mu)=\theta(\mu)$. Differentiating the normalization of the density shows that $\mu=K'(\theta)$, so the <canonical link function> is $(K')^{-1}$ on the admissible parameter interval.
For a <Bernoulli distribution>, the probability mass function can be written as
$$
\mu^y(1-\mu)^{1-y}=\exp\left\{y\log\frac{\mu}{1-\mu}+\log(1-\mu)\right\}.
$$
Thus $\theta=\log(\mu/(1-\mu))$ and $K(\theta)=\log(1+e^\theta)$. \b[The canonical link is the logit:]
$$
\boxed{g(\mu)=\log\frac{\mu}{1-\mu},\qquad 0<\mu<1.}
$$
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