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

To find the inverse of ( y = 2 \cdot 3^x + 1 ):

- Replace ( y ) with ( x ) and ( x ) with ( y ).
- Solve the resulting equation for ( y ).
- The solved equation will be the inverse function.

Steps:

Original equation: ( y = 2 \cdot 3^x + 1 )

Replace ( y ) with ( x ) and ( x ) with ( y ):

( x = 2 \cdot 3^y + 1 )

Solve for ( y ):

( x - 1 = 2 \cdot 3^y )

( \frac{x - 1}{2} = 3^y )

( \log_3\left(\frac{x - 1}{2}\right) = y )

The inverse function is ( y = \log_3\left(\frac{x - 1}{2}\right) ).

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To find the inverse function you have to transform the formula

You have a function:

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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.

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.

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.

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