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about to only mathematics

A

`f_(4)(x)= f_(1)(x)` for all x

B

`f_(1)(x)= -f_(3)(-x)` for all x

C

`f_(2)(-x)= f_(4)(x)` for all x

D

`f_(1)(x)+f_(3)(x)=0` for all x

Text Solution

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The correct Answer is:
B
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CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

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  2. If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (...

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  3. Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...

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  4. If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of ...

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  5. The function f Satisfies the functional equation 3 f (x) +2f ((...

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  6. Let f: RvecR be a continuous and differentiable function such that (f(...

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  7. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

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  8. If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) ...

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  9. If f(x+1/2)+f(x-1/2)=f(x) for all x in R , then the period of f(x)...

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  10. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

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  11. If f(3x+2)+f(3x+29)=AAx in R , then the period of f(x) is 7 (b) 8 ...

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  12. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...

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  13. If f(x)=m a xi mu m{x^3, x^2,1/(64)}AAx in [0,oo),t h e n f(x)={x^2,...

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  14. Find the values of a for which the equation ||x-2|+a|=4 can have four ...

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  15. Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...

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  16. If f(x) is a real=valued function defined as f(x)=1N(1-sinx), then the...

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  17. Let f(x)=x+2|x+1|+x-1|dotIf f(x)=k has exactly one real solution, then...

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  18. The number of solutions of 2cosx=|sinx|,0lt=xlt=4pi, is 0 (b) 2 (c)...

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  19. about to only mathematics

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  20. If log(4)((2f(x))/(1-f(x)))=x, " then "(f(2010)+f(-2009)) is equal to

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