Asked by adly
what is the domain of f(x)=-ln(-x) and the inverse
Answers
Answered by
Steve
ln(x) has domain x > 0
so, -ln(-x) has domain -x > 0 or x < 0, but its range is all real y
y = -ln(-x)
-y = ln(-x)
e^(-y) = -x
x = -e^(-y)
f<sup>-1</sup>(x) = -e<sup>-x</sup>
Note that the domain of f<sup>-1</sup> is all reals, but the range is y < 0
so, -ln(-x) has domain -x > 0 or x < 0, but its range is all real y
y = -ln(-x)
-y = ln(-x)
e^(-y) = -x
x = -e^(-y)
f<sup>-1</sup>(x) = -e<sup>-x</sup>
Note that the domain of f<sup>-1</sup> is all reals, but the range is y < 0
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