# How do you find the inverse of #f(x) = 4(x + 5)^2 - 6#?

No inverse function exists.

Why is this? Let me show you how to compute the inverse if there was one.

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To find the inverse of ( f(x) = 4(x + 5)^2 - 6 ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ), resulting in ( x = 4(y + 5)^2 - 6 ).
- Solve the equation for ( y ) to find the inverse function.

After swapping ( x ) and ( y ), the equation becomes:

[ x = 4(y + 5)^2 - 6 ]

Now, solve for ( y ):

[ x = 4(y + 5)^2 - 6 ] [ x + 6 = 4(y + 5)^2 ] [ \frac{x + 6}{4} = (y + 5)^2 ] [ \pm \sqrt{\frac{x + 6}{4}} = y + 5 ] [ \pm \sqrt{\frac{x + 6}{4}} - 5 = y ]

So, the inverse function is:

[ f^{-1}(x) = \pm \sqrt{\frac{x + 6}{4}} - 5 ]

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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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