预备微积分 · 免费预览
复合函数
函数复合的过程如何从两个函数产生一个新函数？
1. Introduction
Introduction
2. Composing two functions
Composing two functions
3. Composing functions in context
Composing functions in context
4. Composing two formulas
Let p(x) = 3x - 4 and q(t) = t^2 - 1. If r(t) = p(q(t)), what is r(2)?
5. Composition from a graph
With p(0) = -1/2 and q(-1/2) = 2, what is q(p(0))?
6. Composition from a graph twice
A piecewise-linear graph gives p(-1) = -1. What is (p o p)(-1)?
7. Composition from a table
From the tables f(0) = 6 and g(2) = 0, what is (f o g)(2)?
8. When a composition is undefined
With f(0) = 6 and g defined only at inputs 0 through 4, what is g(f(0))?
9. Solving a composition equation
From the table f(1) = 4 and f(3) = 4, and g(0) = 1, g(1) = 3. For which x is f(g(x)) = 4?
10. Chirps to Celsius in one step
Dolbear gives F = 40 + 0.25N and Celsius is C = (5/9)(F - 32). What does the composition H(N) = (5/9)(8 + 0.25N) represent?
11. Composition can be undefined even when both functions are defined
If f and g are both defined everywhere, then g(f(x)) is automatically defined for every x.