Question #16955

Find (a) the domain of f and (b) f−1.
f(x)=ln(2+lnx)
(a) x>............
(b) f−1(x)=...........

Expert's answer

a) ln x so x>0 in other hand 2+ln(x)>0 so ln(x)>-2 so

x>e^(-2)>0

x>e^(-2)

b)f^(-1) can be defined on every point

because for every y y=ln(2+ln(x)) have exactly one solution

e^y=2+ln(x)

ln(x)=e^y-2

x=e^[ e^y-2 ]

x>e^(-2)>0

x>e^(-2)

b)f^(-1) can be defined on every point

because for every y y=ln(2+ln(x)) have exactly one solution

e^y=2+ln(x)

ln(x)=e^y-2

x=e^[ e^y-2 ]

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