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# What is latent function?

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A latent function is an unintended or unrecognized consequence of an institution or social phenomenon. Unexpected negative consequences are typically called latent dysfunctions. School, for example, has the explicit, or manifest, function of educating individuals, but a latent function of teaching students about navigating social structures and relationships and keeping children off the streets for six to 10 hours a day.

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The Prohibition, the banning of all alcohol manufacturing, sales and transportation by constitutional amendment, had several latent functions, such as an increase in the number of pharmacists, legally allowed to obtain medicinal alcohol, an increase in church attendance and clergy (churches were allowed to obtain wine for religious services), and an increase in the number of home distilleries. The grape industry sold bags of grapes with warning labels that warned consumers not to leave them out too long or they would ferment. Home stills could be found at hardware stores, and pamphlets giving instructions on how to make wine could be found at a public library.

Perhaps the worst latent function of the Prohibition was the criminal empire it created. Police made large sums of money in bribes, and criminal activity went relatively unchecked. The plea bargain was introduced, as the court system could not keep up with the influx of violators, and jails overflowed.

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The inverse function of ln(x) is e^x, where e is the mathematical constant e = 2.718. One can easily check that these two functions are inverses of each other by noting that ln(e^x) = e^ln(x) = 1.

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In calculus and related mathematical areas, a linear function is a polynomial function of degree zero or one or is the zero polynomial. In linear algebra and functional analysis, a linear function is a linear map.

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The integral of the secant function is the natural logarithm of the absolute value of the secant of x plus the tangent of x, plus a constant. Expressed in mathematical notation, it reads as the integral of sec x dx = ln |sec x + tan x| + C.