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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
MCQ
A real valued function $f(x)$ satisfies the function equation $f(x - y) = f(x)f(y) - f(a - x)f(a + y)$ where a is a given constant and $f(0) = 1$, $f(2a - x)$ is equal to
  • A
    $f(a) + f(a - x)$
  • B
    $f( - x)$
  • ✓
    $ - f(x)$
  • D
    $f(x)$
✓

Answer

Correct option: C.
$ - f(x)$
c
(c) $f(a - (x - a)) = f(a)f(x - a) - f(0)f(x).....(i)$

Put $x = 0,y = 0$; 

$f(0) = {(f(0))^2} - {[f(a)]^2} \Rightarrow f(a) = 0$

$[ \because f(0) =1 ].$ From $(i)$, $f(2a - x) = - f(x)$.

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