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How do you find the inverse of #y=x^2+2x-1#?

Answer 1

The inverse is #f^-1(x) = sqrt(x+2) -1#

It's quite simple. Always deal with quadratic functions by completing the square and then making #x# the subject in terms of #y#. Replace #y# by #x# to write the final expression for inverse.

Hope that helps, Cheers.

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Answer 2

Benjamin Achtenberg

To find the inverse of (y = x^2 + 2x - 1), follow these steps:

Replace (y) with (x) and (x) with (y) in the equation to get (x = y^2 + 2y - 1).
Rearrange the equation to solve for (y).
This typically involves rearranging the equation into a quadratic equation form and then solving for (y).
Once you have (y) expressed in terms of (x), you have found the inverse function.
Remember to verify the domain and range of the original function and its inverse to ensure they are valid inverses of each other.

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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.