# What is the inverse function of #y=3x^2-5#?

Since we were asked for an inverse function, I've eliminated the non-primary root (a function can not have two values for a single argument value).

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With the default domain, this function has no inverse since it is not one-to-one, but read on...

We can try to find an inverse as follows:

Hence

This is not uniquely defined, so does not define a function, unless...

If we define:

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To find the inverse function of ( y = 3x^2 - 5 ), first, interchange ( x ) and ( y ) to get ( x = 3y^2 - 5 ). Then, solve for ( y ) in terms of ( x ).

[ x = 3y^2 - 5 ] [ x + 5 = 3y^2 ] [ \frac{{x + 5}}{3} = y^2 ] [ y = \pm \sqrt{\frac{{x + 5}}{3}} ]

Therefore, the inverse function is: [ f^{-1}(x) = \pm \sqrt{\frac{{x + 5}}{3}} ]

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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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