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If f(x) is a function such that f(xy)=f(...

If `f(x)` is a function such that `f(xy)=f(x)+f(y) and f(2)=1` then `f(x)=`

A

`x^(2)`

B

`2^(x)`

C

`log_(2)x`

D

`log_(x)2`

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
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  2. If f:R to R is defined as f(x+y)=f(x)+f(y) AA x,y in R and f(1) = 7, f...

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  3. If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

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  4. f: R to R is given by: f(x)= a^(x)/(a^(x) + sqrt(a)) AA x in R, then ...

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  5. If f(x) =((x-a)(x-b))/x and (f(x))/((x-y)(x-z))+ (f(y))/((x-z)(y-z)) +...

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  6. If 2f(x) -3f(1/x)=x^(2), x ne 0, then f(2)=

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  7. If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) " for " x=3, 4, 5, ……...

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  8. If f(x+y,x-y) =xy, then the arithmetic mean of f(x,y) and f(y,-x) is

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  9. Assertion (A) P:f(x) =logx^(3) and g(x) =3 log x are equal functions ...

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  10. Let f(x) =px^(2) + qx^(4) +r. Then for f to be on even function:

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  11. If f(x) =ax^(5) + bx^(3) + cx +d is an odd function, then d=

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  12. f{x) is an even polynomial function. Then sin(f(x)-3x) is

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  13. If f(x) and g(x) are be two functions with all real numbers as their d...

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  14. If f(x) + g(x) = e^(-x) where f(x) is an even function and g(x) is an...

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  15. Assertion (A) : The function f(x) = cos x is symmetric about the line ...

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  16. A function whose graph is symmetrical about the y-axis is given by:

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  17. The graph of the function y = f(x) is symmetrical about the line x = 2...

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  18. If f:{1, 2, 3,……}rarr{0, pm1, pm2, …..} is defined by f(x)={{:(n//2,"...

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  19. If f(x)=(4-(x-7)^(3))^(1/5), then f^(-1)(x)=

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  20. If f:[1, infty) to [2, infty) is given by f(x) =x+1/x, then f^(-1)(x)=

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