Verified Solution • 2025–26 Session moderate

QJEEM05Ma1ac9: JEE Main 2005 Mathematics - Class 11 JEEM05Ma1ac9 Solution: A real valued function f(x) satisfies the functional equation…

A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to

Multiple Choice Options

  • A f(x)
  • B #NAME?
  • C f(a) + f(a - x)
  • D f(- x)

Step-by-Step Verified Solution

f(2a−x)=f(a−(x−a))

=f(a)f(x−a)−f(0)f(x)

=f(a)f(x−a)−f(x)

=−f(x)

[ as x=0,y=0,f(0)=f2(0)−f2(a)

⇒f2(a)=0⇒f(a)=0]

⇒f(2a−x)=−f(x)

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