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A-level functions question

F(x) = 2 - √x for x ≥ 0.
Given that the equation | f(x) | = k has two distinct roots, determine the possible values of the constant k.

Not sure what to do here, if someone could work through this it would be greatly appreciated.

Thanks
~Bradley.

Reply 1

Pulkpull

A good start would be to sketch the graph. Do you know how to go about doing that?

Reply 2

Bjwert

Yes, the exam paper includes a diagram of the graph.

Reply 3

maxfire

Start by drawing x=k, and find y in terms of k?

Reply 4

Pulkpull

Are you given the graph of f(x) or |f(x)|? If the former, you should sketch |f(x)| and think about the conditions that need to be fulfilled for |f(x)| = k to have two distinct roots. This will occur when y = |f(x)| and y = k intersect, so from looking at the graph you should be able to see the range of values.