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

Answer 1

Liam Brennan

Inverse function of #y=4^x# is #y=0.7213lnx#

As #y=4^x#

#x=log_4y=lny/ln4=0.7213lny#

Hence inverse function of #y=4^x# is

#y=0.7213lnx#

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Answer 2

Sadie Alexander

To find the inverse of ( y = 4^x ), follow these steps:

Replace ( y ) with ( x ) and ( x ) with ( y ): ( x = 4^y ).
Solve this equation for ( y ):

[ x = 4^y ] [ \log_4(x) = y ]

So, the inverse function of ( y = 4^x ) is ( y = \log_4(x) ).

Yes, the inverse function is a function because for every input ( x ) in the domain of ( y = 4^x ), there exists a unique output ( y ) in the domain of its inverse function, and vice versa.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.