Find the inverse function... So, I have the function f ( x ) =

taghdh9

taghdh9

Answered question

2022-06-21

Find the inverse function...
So, I have the function
f ( x ) = 2 x 2 x 2 .
I tried finding the inverse function the usual way I do, but I guess I'm stuck with these degrees. So far, I've come to this form
y = 2 2 x 2 0 2 x + 1 .
When I used Wolfram Alpha Inverse Function Finder, it gave me this solution
f 1 ( x ) = log ( x x 2 + 1 ) / log ( 2 ) .
I have no idea how it god those logs, please help me :D

Answer & Explanation

Cristopher Barrera

Cristopher Barrera

Beginner2022-06-22Added 24 answers

Hint:
2 x 2 x 2 = y ( 2 x ) 2 2 y 2 x 1 = 0.
boloman0z

boloman0z

Beginner2022-06-23Added 10 answers

Note that
f ( x ) = e x log 2 e x log 2 2 = cosh ( x log 2 ) = y ,
so that
x = 1 log 2 arccosh  y .

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