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组合函数
我们怎样通过对给定函数作加、减、乘、除来构造新函数？
1. Introduction
Introduction
2. Arithmetic with functions
Arithmetic with functions
3. Combining functions in context
Combining functions in context
4. Adding function values
With f(3) = 20 and g(3) = 2, what is h(3) where h = f + g?
5. Difference and product of functions
With f(1) = 4, g(1) = 3, f(-1) = 1 and g(-1) = 3, what is (f * g)(-1)?
6. Where a quotient is undefined
For functions f and g given by graphs, where is (f/g)(x) undefined?
7. Zeros of a product
Where is (f * g)(x) = 0 for functions given by graphs whose zeros are f(7/3) = 0, g(-2) = 0 and g(3) = 0?
8. Building a composite meaning from two functions
If f(v) gives gallons per mile at speed v and f(60) = 0.04, what does that value mean?
9. Reciprocal fuel rate
With f(60) = 0.04 gallons per mile, what is g(60) where g(v) = 1/f(v)? Give miles per gallon.
10. Average rate of fuel consumption
With f(60) = 0.04 and f(70) = 0.045 gallons per mile, what is the average rate of change of f on [60, 70]?
11. A quotient fails only where its denominator is zero
The quotient f/g is undefined exactly where the denominator g equals zero.