Solving a Functional Equation Involving [f(x)]^2

On first meeting functional equations of the type [f(x)]^2 + af(x) = g(x) where g(x) is known and f(x) is the unknown we are required to find, students are forgiven for scratching their heads. But in fact, as we show in this video where we answer two such questions, they are not in the slightest bit scary and in fact can be solved with fairly elementary maths. Of course it is often the case that once shown the method, finding the solution becomes easy and it is certainly the case here.

As a bonus, at 6:16 we discuss a fairly popular (but awful) method to solve a very limited subset of these types of questions, which we certainly don't recommend but is worth knowing (if only to reject it).

Questions such as these are common in Maths Olympiads and College Entrance Tests - as such, the methods employed in this video to solve them are well worth remembering.

For more videos on functional equations see our playlist 'Functional Equations'

For more videos on functions generally see our playlist 'Functions'

For more videos on Maths Olympiads, see our playlist 'Maths Olympiads'

For more videos on College Entrance Tests see our playlist 'UPCAT and Other CETs'

For more videos on JEE Main see our playlist 'JEE Aspirant'