# How do I find the inverse function of #f(x)=e^(3x)-4 #? And what is it's range ?

Change the x and ys to find the inverse algebraically.

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To find the inverse function of ( f(x) = e^{3x} - 4 ), we first swap ( x ) and ( y ) to get ( x = e^{3y} - 4 ). Then, solve for ( y ) to find the inverse function.

[ x + 4 = e^{3y} ]

[ \ln(x + 4) = 3y ]

[ y = \frac{1}{3} \ln(x + 4) ]

The range of the function ( f(x) = e^{3x} - 4 ) is ( (-4, +\infty) ), because ( e^{3x} ) is always positive, and subtracting 4 shifts the range down by 4 units.

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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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