Home > Precalculus > Function Composition

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

Answer 1

Serenity Johnson

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) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Caleb Alexander

To find the inverse function you have to transform the formula #y=f(x)# to #x=f(y)#. For this example see explanation:

You have a function:

#y=2*(3^x)+1#

Now we are trying to calculate #x#:

#y-1=2*3^x#

#(y-1)/2=3^x#

#x=log_3 ((y-1)/2)#

Answer: The inverse function is: #f(x)=log_3((x-1)/2)#

Note: In the answer you usualy write the inverse function as: #y=f(x)#.

By signing up, you agree to our Terms of Service and Privacy Policy

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.