问一道数学题

use function notation to write g(x)=7+2|x+3| in terms of f(x)=|x-2|

绝对值得考虑进去吧。

x-2 = +/-f(x) plug in g(x) = 7 + 2 | +/- f(x) + 5 | = 7 + 2 | f(x) +/- 5 |

g(x)=7+2f(x+5)

g(x)=7+2f(x+5)

ice2008 发表于 2023-09-17 22:44

你的对。
我的推导，过程有错吗？

g(x)=7+2f(x+5)

ice2008 发表于 2023-09-17 22:44

👍

回复 3楼youyouzou的帖子
This is not a function. There has to be a unique value as an output for each input in the domain.

這道題用4樓的答案，應該理解成 write g(x) in terms of f(.), where f(x)=|x-2|. 要不然literally in terms of "f(x)" 則用分段函數可以寫成三段，where x>=2, -3<=x<2, x<-3.

回复 3楼youyouzou的帖子
This is not a function. There has to be a unique value as an output for each input in the domain.
pinwheel 发表于 2023-09-17 22:54

明白了。
g(x) = 7 + 2 ｜f(x) + 5 | 或者 g(x) = 7 + 2 ｜f(x) - 5 |
两者都不能完match原来的描述
如下写，算不算对捏？ g(x) = 7 + 2 ｜f(x) + 5 | when x >=2, 7 + 2 ｜f(x) - 5 | when x < 2