7.71 The function $f(x)=x+\frac{1}{x}$ defined on the interval $(0,+\infty)$
(A) is an increasing function.
(B) is a decreasing function.
(C) is a function that first decreases and then increases.
(D) is a function that first increases and then decreases.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] Let $0f\left(x_{1}\right)$.
Therefore, on the interval $(0,1]$, $f(x)$ is a decreasing function; on the interval $[1,+\infty)$, $f(x)$ is an increasing function.
Hence, the correct choice is $(C)$.