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If f(a)=log.(2+a)/(2-a)" for " 0lt a lt2...

If `f(a)=log.(2+a)/(2-a)" for " 0lt a lt2` then `(1)/(2)f((8a)/(4+a^(2)))=`

A

`f(a)`

B

`2f(a)`

C

`(1)/(2)f(a)`

D

`-f(a)`

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. If f(x)=log.(1+x)/(1-x) then f((x(1)+x(2))/(1+x(1)x(2)))=

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  2. If f(x)=log.(1-a)/(1+a)" for " 0ltalt1 then f((2a)/(1+a^(2)))=

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  3. If f(a)=log.(2+a)/(2-a)" for " 0lt a lt2 then (1)/(2)f((8a)/(4+a^(2)))...

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  4. If e^(f(x))=(10+x)/(10-x), x in (-10, 10) and f(x)=kf ((200x)/(100+x^(...

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  5. For any integer n ge1, the number of positive divisors of n is denoted...

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  6. If NN denotes the set of all positive integers and if f:NN rarrN is d...

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  7. If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x when [x] is the step function, then...

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  8. If f(x) is a polynomial fin x( gt0) satisfying the equation f(x)+f(1//...

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  9. If f(x) is a polynomial function x>0 such that f(x)f(1//x)=f(x)+f(1//x...

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  10. If f(x) is a polynomial function such that f(x)f((1)/(x))=f(x)+f((1)/(...

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  11. If f(x) is a function such that f(x+y)=f(x)f(y) and f(5) =125 " then "...

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  12. 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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  13. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

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  14. If f(x)=sin(logx), then f(xy)+f(x//y)-2f(x)cos (logy)=

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  15. If f(n)(x)-(tan.(x)/(2))(1+secx)(1+sec 2x)……(1+sec2^(n)x) then which o...

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  16. If f:A rarrR is defined as f(x)=x^(3)+1 and A={1, 2, -1, -2, 0} then t...

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  17. If f:ArarrR is defined as f(x)=cosx and A={0, pi//6, pi//4, pi//3} the...

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  18. If f:ArarrR is defined as f(x)=tan(x//2) and A{pi//2, pi//3, 2pi//3} t...

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  19. If A={3, 0, 1, 2} and f:A rarr B is an onto function defined by f(x)=3...

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  20. If f:[2, oo)rarrB defined by f(x)=x^(2)-4x+5 is a bijection, then B=

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