How do you find the inverse of #g(x) = y = (x-6)^5#?

Answer 1

James Allen

#g^-1(x) = x^(1/5)+6 #

#g(x)=y=(x-6)^5# or

#y^(1/5)=(x-6) or x = y^(1/5)+6 # or

#g^-1(y) = y^(1/5)+6 # or

#g^-1(x) = x^(1/5)+6 # [Ans]

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Answer 2

Serenity Johnson

To find the inverse of the function ( g(x) = (x - 6)^5 ), follow these steps:

Replace ( g(x) ) with ( y ).
Swap the variables ( x ) and ( y ).
Solve the resulting equation for ( y ).
Replace ( y ) with ( g^{-1}(x) ) to express the inverse function.

Let's proceed with these steps:

Start with ( g(x) = (x - 6)^5 ).
Replace ( g(x) ) with ( y ) to get ( y = (x - 6)^5 ).
Swap ( x ) and ( y ) to get ( x = (y - 6)^5 ).
Solve for ( y ): [ x = (y - 6)^5 ] [ \sqrt[5]{x} = y - 6 ] [ y = \sqrt[5]{x} + 6 ]

So, the inverse function of ( g(x) ) is: [ g^{-1}(x) = \sqrt[5]{x} + 6 ]

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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.