Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsFunctional EquationHard3 minQB

MathematicsHardsingle choice

Let $f : R \to R$ satisfy $f (x) + 2 f (1 - x) = x^{2} + 1$ . For which $m$ does $f (∣ x ∣) = m$ have exactly two solutions?

Answer:

Solution:

$f (x) = (x^{2} - 4 x + 3) /3$ ; analysis of $f (∣ x ∣)$ gives $(1, \infty) \cup {- 1/3}$ .

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Functional Equation

⏱ 3mℹ️ Source: QB

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