Let f be a function such that f ( x + f ( y )) = f ( x ) + y ; ∀ x , y ∈ R then f ( 2013 ) = ____

Put y = x ⇒ f ( x + f ( x )) = f ( x ) + x ⇒ f ( t ) = t (Identity function)

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MathematicsFunctionsFunctional EquationEasy2 minQB

MathematicsEasysingle choice

Let f be a function such that $f (x + f (y)) = f (x) + y; \forall x, y \in R$ then $f (2013) =$ $____$

Answer:

Solution:

Put $y = x \Rightarrow f (x + f (x)) = f (x) + x$ $\Rightarrow f (t) = t (Identity function)$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

⏱ 2mℹ️ Source: QB

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