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# C3 maths help! rep to best explanation watch

1. I'm struggling with this question:
given that equation |f(x)|=k has two distinct roots, determine the possible values of k.

f(x)=2-sqrt of x

Thank you!
2. (Original post by Astana)
I'm struggling with this question:
given that equation |f(x)|=k has two distinct roots, determine the possible values of k.

f(x)=2-sqrt of x

Thank you!
Best if you sketch then observe for which the horizontal line intersects it twice.
3. (Original post by RDKGames)
Best if you sketch then observe for which the horizontal line intersects it twice.
the answer is 0<k<2, but I'm really unsure how to get this
4. (Original post by Astana)
the answer is 0<k<2, but I'm really unsure how to get this
Well, have you made the sketch?
5. (Original post by RDKGames)
Well, have you made the sketch?
yes, but I still don't understand it. The intercept with the y-axis is at 2, and it cuts the x-axis at 4
6. Draw f(x) = 2 - root x.

It's basically -root x + 2 so that's the transformations.

Then |f(x)| would be just the negative part flipped over the y axis. Notice that now |f(x)|=k will have 2 solutions if k is between 0 and 2. Drawing any straight horizontal line here will have 2 solutions thefore 0<k<2.
7. (Original post by Astana)
yes, but I still don't understand it. The intercept with the y-axis is at 2, and it cuts the x-axis at 4
So then if you draw a straight horizontal line on the graph, where must it be for it to intersect your graph twice?
8. (Original post by RDKGames)
So then if you draw a straight horizontal line on the graph, where must it be for it to intersect your graph twice?
it can't intersect it twice because it's not a quadratic
9. (Original post by Astana)
it can't intersect it twice because it's not a quadratic
Not sure where you pulled this from as a reason.

The red curve represents and the blue line represents . These two will intersect twice when takes which values...?

10. (Original post by RDKGames)
Not sure where you pulled this from as a reason.

The red curve represents and the blue line represents . These two will intersect twice when takes which values...?

oh, I see, larger than 0 but equal or less than 2.

Thank you

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Updated: February 11, 2018
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