Exercise 1 solution

Manifest function (functionalism): a hospital treats the sick and injured. That is its intended, recognised purpose, in Merton's sense as described on Wikipedia's Structural functionalism page.

Latent function (functionalism): it also brings together people from many backgrounds in one place and creates working relationships among staff, much as the page's own example says schools build social networks as a side effect. This one is my own extension of the page's example (check).

Lens used: both of the above use functionalism, because both ask what the institution contributes to the wider society.

What functionalism finds hard to explain: the page lists the criticism that the approach ignores inequalities of race, gender and class and struggles to explain conflict. A functionalist account of a hospital says what it does for the whole, but it does not by itself explain why some groups get care sooner or better than others. A conflict-theory question ("who has access, and who decides?") would pick that up.

Note: the example choices are mine and several answers would be acceptable. What matters is that the manifest function is the stated purpose, the latent one is an unintended side effect, and the criticism is one the chapter actually lists.