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If a function f satisfies the conditions...

If a function f satisfies the conditions `f(x+y)=f(x)+f(y)AA, x,y in R`, then f is :

A

an even function

B

an odd function

C

neither even nor odd

D

none of these

Text Solution

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The correct Answer is:
B
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ARIHANT SSC-FUNCTIONS AND GRAPH-INTRODUCTORY EXERCISE - 17.2
  1. If f(x)=((x-1)/(x+1)), then f(f(ax)) in terms of f(x) is equal to:

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  2. If f(x)=(x)/(sqrt(1+x^(2))), then fofof(x) is equal to:

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  3. If f(x)={{:(1+|x|,,,xlt-1),([x],,,xge-1):} Also, [.] is greatest inte...

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  4. If f(x)=x^(n), n in N and (gof)(x)=ng(x), then g(x) can be :

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  5. Let f:Nrarr R,f(x)=2x-1 g:z rarrR,g(x)=(x^(2))/(2), then (gof)(0) is...

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  6. Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(xne0), then f(x) is equal to :

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  7. Let f(x)=sqrt(x^(5)), then f(5x) is equal to :

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  8. If f(x)=4x-5,g(x)=x^(2) and h(x)=(1)/(x), then f(g(h(x))) is :

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  9. If [x] denotes greatest integer function less than or equal to x and {...

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  10. If the graph of the function f(x)=(a^(x)-1)/(x^(n)(a^(x)+1)) is symmet...

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  11. f(x)=ln(x+sqrt(x^(2)+1)) is :

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  12. If a function f satisfies the conditions f(x+y)=f(x)+f(y)AA, x,y in R,...

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  13. Which of the following function is an even function?

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  14. Which of the following function is odd ?

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  15. Which of the following function is even function?

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  16. If f(x)=root(3)((1-x^(2)))+root(3)((1+x^(2))), then f(x) is :

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  17. Which of the following function is an odd function?

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  18. The function f(x)=(x)/(e^(x)-1)+(x)/(2)+1 is :

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

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  20. Given f(x)=(1)/((1-x)).g(x)=f(f(x)) and h(x)=f(f(f(x))), then the valu...

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