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

To find an inverse, switch x and y (or f(x)).

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To find the inverse of the function ( f(x) = x^2 + x ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap the roles of ( x ) and ( y ): ( x = y^2 + y ).
- Solve the equation obtained in step 2 for ( y ).
- Replace ( y ) with ( f^{-1}(x) ) to express the inverse function.

Here's the process:

[ x = y^2 + y ]

[ x = y(y + 1) ]

[ y(y + 1) = x ]

[ y^2 + y - x = 0 ]

Using the quadratic formula:

[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), we have:

[ y = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

So, the inverse function ( f^{-1}(x) ) is:

[ f^{-1}(x) = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

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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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