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How do you find the inverse of #f(x)=3^(x-1)-2#?

Answer 1

Chloe Alexander

To find the inverse of ( f(x) = 3^{(x-1)} - 2 ), we swap ( x ) and ( y ) and solve for ( y ):

[ x = 3^{(y-1)} - 2 ]

[ x + 2 = 3^{(y-1)} ]

[ \log_3(x + 2) = y - 1 ]

[ y = \log_3(x + 2) + 1 ]

So, the inverse function is ( f^{-1}(x) = \log_3(x + 2) + 1 ).

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Answer 2

Cora Alexander

#x=2.096log(f(x)+2)+1#

#f(x)=3^(x-1)-2# #f(x)+2=3^(x-1)# taking log both sides #log(f(x)+2)=log3^(x-1)# #log(f(x)+2)=(x-1)*log3# #x-1=log(f(x)+2)/log(3)# #x=2.096log(f(x)+2)+1#

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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.