预备微积分 · 免费预览
反函数(续)
说一个给定函数有反函数,是什么意思?
1. Properties of an inverse function
Properties of an inverse function
2. Summary
Summary
3. Rainfall rate three hours in
A storm's rainfall rate is g(t) = 4/(t+2) + 1 cm/hr. What is the rate at t = 3 hours? Give the decimal.
4. Rainfall rate's average change
For g(t) = 4/(t+2) + 1, the average rate on [3,5] is -4/35 cm/hr^2. What does the sign and units say?
5. Inverse rainfall function value
For g(t) = 4/(t+2) + 1, solve g(t) = 9/5 for t. Give the exact integer.
6. A rate the model never reaches
Can g(t) = 4/(t+2) + 1 ever equal 1 centimeter per hour during the storm?
7. Reflecting to read an inverse
If the point (2.5, -3.5) lies on the inverse function's graph, which point lies on the original function?
8. Rising level and invertible volume
A conical tank fills so the water height is h = 0.25t. Why does the volume model have an inverse?
9. Inverse of the chirp-to-Celsius function
With C = 40/9 + (5/36)N, solving for N gives N = (36/5)C - 32. What is N when C = 18?
10. A quantity that rises strictly is invertible in time
If a quantity rises strictly as time passes during a process, the quantity can be used to recover the elapsed time uniquely.