Function Problem, Type II, Rule 2

Hi, are you able to provide an example question for the “Function Problem” section in regards to Type II, Rule 2: “taken the even root of a negative number”. I do not understand what that means so a practice question would be very useful. Thanks!

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Hi, Ana2! Orion here to answer your question.

One of the two ways a function can be undefined on the GRE is when the function tries to take the even root of a negative number. This is most common with a square root, but it could also technically be a fourth root or a sixth root or an eighth root, etc. Hence, “even” root.

On the other hand, a negative number poses no problem for an odd root, like a cube root. For instance, the cube root of -8 is -2. We know this is true because the process is reversible: -2 cubed is -8. However, the square root of -4 can’t be -2, because the process isn’t reversible: -2 squared is positive 4 (not -4). In point of fact, there is no value that – when squared – equals -4. So we say that the square root of -4 is undefined.

Hope this helps!


Hi, that really helps wrap my head around it. Are you able to show how this would work in an example? What I love about the textbook are the examples that really illustrate how a problem can be used with techniques. Thanks!

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Hey @Ana2, that’s a great suggestion.

I’ve discussed this with @Orion and we’ll add an example to the textbook. We’re working on a few things right now and we expect to make this update towards the end of next week!

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Hey @Ana2, we were able to get to this sooner than expected - let us know if the updates clear this up!

Function problems | Achievable GRE

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