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Find a real function f:R→R such that f(f(x))=−x?


An important piece of information is: Theorem: f is not continuous. Proof: Observe that f is invertible, because. f(f(f(f(x))))=f(f(−x))=x. and so fff=f−1.


For more information, see Find a real function f:R→R such that f(f(x))=−x?

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Linear Transformations


to say: the level set of the function F(x, y) = x2 +y2 at height 1. That is ... x = f(t) y = g(t). Surfaces in R3: Three descriptions. (1) Graph of a function f : R2 → R. (That is: z = f(x, y).) ... The linear transformation defined by D has the following effect: Vectors are. ... Example 1: Let A be a (3 × 2)-matrix, and let B be a (2 × 4)-matrix.


For more information, see Linear Transformations