1) If f:R→R is a function satisfying the property f(2x+3) + f(2x+7) = 2, x#R, then the period of f(x) is?
2)If f(x) = sin(\sqrt{\left[\lambda \right]}x) is a periodic function with period \prod{}, where [.] represents greatest integer, then a) \lambda \epsilon [4,5) b) \lambda \varepsilon [4,5] c) \lambda =4,5 d) none of these
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4 Answers
13) If a real valued function f(x) satisfies the eqn f(x+y)= f(x) + f(y) for all real x,y, then f(X) is
a) a periodic function
b) an even function
c) an odd function
d) none of these
1f ( 2 x + 3 ) + f ( 2 x + 7 ) = 2
Replace " x " by " x + 2 " .
f ( 2 x + 7 ) + f ( 2 x + 11 ) = 2
Subtracting ,
f ( 2 x + 3 ) = f ( 2 x + 11 )
Hence , f ( x ) is a function with period 8 .