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C3 maths help! rep to best explanation

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!

Reply 1

RDKGames

Study Forum Helper

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

|2- \sqrt{x}|

then observe for which

k

the horizontal line

y=k

intersects it twice.

(edited 6 years ago)

Reply 2

Astana

Original post by RDKGames

Best if you sketch

|2- \sqrt{x}|

then observe for which

k

the horizontal line

y=k

intersects it twice.

the answer is 0<k<2, but I'm really unsure how to get this

Reply 3

RDKGames

Study Forum Helper

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?

Reply 4

Astana

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

Reply 5

thekidwhogames

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.