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How do you find the inverse of #f(x)=4^x# and is it a function?

Answer 1

Ariana Alvarez

#f^-1(x)=log_4 x#---> is a function.

#y=4^x#

#x=4^y#---> Switch x and y

#logx=log 4^y#

#log x =y log 4#

#y=log x/log4#

#y=log_4 x#--> Inverse

#f^-1(x)=log_4 x#

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Answer 2

Christian Antunez

To find the inverse of ( f(x) = 4^x ), we first interchange the roles of ( x ) and ( y ), then solve for ( y ).

So, let ( y = 4^x ).

Interchange ( x ) and ( y ): ( x = 4^y ).

Now, solve for ( y ): [ \log_4{x} = y ]

Hence, the inverse function is ( f^{-1}(x) = \log_4{x} ).

Yes, ( f(x) = 4^x ) is a function because for each input ( x ), there is exactly one output ( f(x) ).

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Answer 3

Sophie Adams

To find the inverse of the function ( f(x) = 4^x ), we switch the roles of ( x ) and ( y ) and solve for ( y ).

Replace ( f(x) ) with ( y ): ( y = 4^x ).
Swap ( x ) and ( y ): ( x = 4^y ).
Solve for ( y ): [ \log_4(x) = y ]

Thus, the inverse function of ( f(x) = 4^x ) is ( f^{-1}(x) = \log_4(x) ).

As for whether the inverse function is a function, yes, ( f^{-1}(x) = \log_4(x) ) is a function. Each input ( x ) corresponds to exactly one output ( y ), which fulfills the definition of a function.

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Answer from HIX Tutor

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