What is the inverse of #f(x) = 2^sin(x)# ?

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What is the inverse of #f(x) = 2^sin(x)# ?

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Answer 1 · 2015-10-29T22:30:20

I found: #y=arcsin[log_2(f(x))]#

Explanation:

I would take the #log_2# on both sides:
#log_2f(x)=cancel(log_2)(cancel(2)^(sin(x)))#
and:
#log_2f(x)=sin(x)# isolating #x#:
#x=arcsin[log_2(f(x)]#
So that our inverse function can be written as:
#y=f(x)=arcsin[log_2(f(x))]#

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What is the inverse of #f(x) = 2^sin(x)# ?

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