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

B

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

C

`f(x_(1)).f(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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DISHA PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE - 1
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  5. If f(x)=xandg(x)=|x|, then what is (f+g)(x) equal to ?

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  6. If f(x) = e^(-x), then (f (-a))/(f(b)) is equal to

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  7. If P={x in R : f(x)=0} and Q={x in R : g(x)=0 }, then PuuQ is

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  8. The domain of the function f(x) = (|x + 3|)/(x + 3) is

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  9. let f(x)=sqrt(1+x^2) then

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  10. The function f(x)=log(10)((1+x)/(1-x)) satisfies the equation

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  11. If f (x + y) = f(x) + 2y^(2) + kxy and f(a) = 2, f(b) = 8, then f(x) ...

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  12. Let f1(x)={x, x leq x leq 1 and 1 x gt1 and 0,otherwise f2(x) =f1 (...

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

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  14. Let f(x) = (alpha x^(2))/(x + 1), x ne - 1 , The value of alpha for wh...

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  15. The domain of the function f(x) = exp ( sqrt(5x - 3 - 2x^(2))) is

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  16. If f : R rarr R be defined as f(x) = 2x + |x|, then f(2x) + f(-x) - f...

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  17. Domain of definition of the functioni f(x)=3/(4-x^(2))+log(10)(x^(3)-x...

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  18. Which of the following is wrong ?

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  19. Let f(x) be defined on [-2,2] and is given by f(x) = {{:(x+1, - 2l...

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  20. The domain for which the functions defined by f(x)=3x^(2)-1 and g(x)...

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