Home > Precalculus > Function Composition

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

Answer 1

Madelyn Anderson

To find the inverse of ( y = \ln(x + 2) ), switch the roles of ( x ) and ( y ) and solve for ( y ).

Start with the original equation: ( y = \ln(x + 2) ).
Swap ( x ) and ( y ): ( x = \ln(y + 2) ).
Solve for ( y ): ( e^x = y + 2 ).
Subtract 2 from both sides: ( y = e^x - 2 ).

So, the inverse function is ( y = e^x - 2 ).

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

Answer 2

Madelyn Anderson

#y = e^x-2#

The easiest way to find the inverse of a function is to swap #x# and #y# and solve for #y#:

#y = ln(x+2) -> x = ln(y+2)#

We then raise #e# to the power of both sides to remove the natural logarithm:

#x = ln(y+2) -> e^x = y+2#

And subtract #2# to isolate #y#:

#e^x = y+2 -> e^x-2 = y#

Making our final answer #y = e^x-2#

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.