I'm having trouble with this question, any help is appreciated
Given f(x)=e^(-e^x) and g(x) =1/2 sqr(x+4), which of the following is in the domain of (f^-1composed g)(x)?
a. −1
b. 0
c. 1
d. 5
e. None of the above
Pre-Calc question about domain?
2015-09-02 2:06 am
回答 (1)
2015-09-02 3:09 pm
✔ 最佳答案
f = e^(-e^x)ln f = - e^x
- ln f = e^x
x = ln ( - ln f )
Hence,
f ^ -1 = ln ( - ln x )
g = (1/2)√(x+4)
f ^ -1。g (x)
= f ^ -1 ( g(x) )
= f ^ -1 ( (1/2)√(x+4) )
= ln { - ln [ (1/2)√(x+4) ] }
(1)
x+4 > 0
x > - 4
(2)
- ln [ (1/2)√(x+4) ] > 0
ln [ (1/2)√(x+4) ] < 0
(1/2)√(x+4) < 1
√(x+4) < 2
x+4 < 4
x < 0
Thus, - 4 < x < 0
Ans: a
收錄日期: 2021-05-02 14:12:20
原文連結 [永久失效]:
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