I don't understand where the rational notation or the fractional notation came from.. Very confused!

Vivian,

There is a mistake in the problem description. The fractional notation is missing:

g(x) = (2x-3)¼ + 1

We have corrected this error. The fix will be in the next release.


Thanks for letting us know!

- Arcadia

How do you know when to change from fractional notation to radical notation?and where did the equation come from because I'm completely confused?

Sam,

You can use either radical notation or fractional notation--whatever you feel most comfortable with for a given expression.

You just have to remember that X raised to the (1/2) power is the same as the square root of X (√X).

If you have X raised to the (1/3) power, that's the same as the "cube root" of X (which is written as a square root symbol with a little number "3" nested in the "v" shape on the outside of the radical symbol).

Does this make sense?

For this question, it says since the root is even everything under the radical has to be greater than or equal to 0. Does it mean that if the root was odd, everything under the radical would be less than 0?

Dodie, that is not the case. If the root was odd (say, 3 or cubed), then everything under the radical could either be positive or negative.

For example, we can ask: what is the cubed root of (-8)? We can also ask: what is the cubed root of 8?

But we can't ask, what is the square root of (-8)? At least not using real numbers.

Since it is a fourth root, the radicand has to be positive or there is no solution at all. So we know that 2x-3 is greater than or equal to 0, yielding us choice (C).