A real value function f(x) satisfie...
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A real value function f(x) satisfies the function equation f(x - y) = f(x) f(y) - f(a - X) Ta 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) (C)-f(x) (D) f(x)

JEE/Engineering Exams
Maths
Solution
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Put ( x=y=0 ) ( f(0)=f(0) f(0)-f(a) f(a) ) ( begin{array}{ll}1= & 1-(f(0))^{2} Rightarrow & f(a)=0end{array} ) Let ( (2 a-x)=a-(a-x) ) ( a-(x-a) ) [ begin{array}{c}P omega t x=9 & y=x-aend{array} ] ( f(2 a-x)=f(a) f(x-a)-f(0) f(x) ) ( f(2 a-x)=frac{1}{0}-f(x) )
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