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The function f(x)=log(10)((1+x)/(1-x)) s...

The function `f(x)=log_(10)((1+x)/(1-x))` satisfies the equation

A

`f(x+2)-2cd(x+1)+f(x)=0`

B

`f(x+1)+f(x)=f(x(x+1))`

C

`f(x_(1)(x_(2))=f(x_(1)+x_(2))`

D

`f(x_(1))+f_(x_(2))=f((x_(1)+x_(2))/(1+x_(1)x_(2)))`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA-REAL FUNCTIONS -Exercise
  1. The function f(x)=log(10)((1+x)/(1-x)) satisfies the equation

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  2. I fy=f(x) satisfies the condition f(x+1/x)=x^2+1/(x^2)(x!=0) then f(x...

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  3. If f(x+2y , x-2y)=x y , then f(x,y) equals

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  4. If f(x)=x-(1)/(x), x ne 0 then f(x^(2)) equals.

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  5. A polynomial function f(x) satisfies the condition f(x)f((1)/(x))=f...

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  6. The function f(x) = max {(1 - x), (1 + x), 2}, x in (- oo, oo) is equi...

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  7. If f(x)=x^(3)-x and phi (x)= sin 2x , then

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  8. Let f(x)=min{x,x^2}, for every x in R. Then

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  9. The domain of the function f(x) given by f(x)=(sqrt(4-x^(2)))/(sin^(-1...

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  10. The domain of the function f(x)=sqrt({(-log0.3(x-1))/(-x^2+3x+18)})...

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  11. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

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  12. If f : R -> R is defined by f(x) = 1 /(2-cos3x) for each x in R then t...

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  13. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

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  14. The domain of definition of the function f(x)=(1)/(sqrt(|x|-x)) is

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  15. The set of values of x for which the function f(x)=(1)/(x)+2^(sin^(...

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  16. The function f(x)=log(10)(x+sqrt(x^(2))+1) is

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  17. The function f(x)= cos{log(10)(x+sqrt(x^(2)+1)} , is

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  18. f(x)=sqrt(sin^(- 1)(log2x))

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  19. The function f(x)=sqrt(cos(sinx))+sin^-1((1+x^2)/(2x)) is defined for ...

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  20. The function f(x)=|cos| is periodic with period

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