# How do you find the inverse of #f(x)=sqrt(x+1) + 3# and is it a function?

The inverse of a function can be found algebraically by switching the x and y values.

This is a quadratic, therefore it is a function.

Hopefully this helps!

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To find the inverse of the function ( f(x) = \sqrt{x + 1} + 3 ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap the roles of ( x ) and ( y ): ( x = \sqrt{y + 1} + 3 ).
- Solve for ( y ).
- Square both sides to eliminate the square root: ( (x - 3)^2 = y + 1 ).
- Subtract 1 from both sides: ( y = (x - 3)^2 - 1 ).

The inverse function is ( f^{-1}(x) = (x - 3)^2 - 1 ).

Yes, the inverse function is a function because each input value ( x ) corresponds to exactly one output value ( y ), satisfying the vertical line test. Therefore, both the original function and its inverse are functions.

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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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