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

Answer 1

Christian Antunez

To find the inverse of ( y = e^{3x} + 2 ), you switch the variables ( x ) and ( y ) and then solve for ( y ).

Rewrite the equation as ( x = e^{3y} + 2 ).
Subtract 2 from both sides to isolate the exponential term: ( x - 2 = e^{3y} ).
Take the natural logarithm of both sides: ( \ln(x - 2) = 3y ).
Finally, solve for ( y ): ( y = \frac{\ln(x - 2)}{3} ).

So, the inverse of ( y = e^{3x} + 2 ) is ( y = \frac{\ln(x - 2)}{3} ).

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Answer 2

Elias Ackerman

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

Let #y= e^(3x) + 2# rearrange #y - 2 = e^(3x)# take the natural log of both sides #ln(y-2) = 3x; x= 1/3 ln(y-2) #

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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.