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If f(x)=3^(-x)-1, for -1 le x lt0, =ta...

If `f(x)=3^(-x)-1`, for `-1 le x lt0,`
`=tan(x//2), " for "0lexltpi`
`=(x)/(x^(2)-2)," for "pilexlt6,` then `f(-1)+f(pi//6)+f(5)=`

A

0

B

`(27)/(23)-sqrt3`

C

`(27)/(13)+sqrt3`

D

`(97)/(23)-sqrt3`

Text Solution

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. f(x)=4x-1, " if " x gt4 =x^(2)-2, " if " -2 le x le 3 =3x+4," if "...

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  2. Let f: R rarrR be defined by f(x)={{:(x+2, (xle-1)),(x^(2), (-1lexle1)...

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  3. If f(x)=3^(-x)-1, for -1 le x lt0, =tan(x//2), " for "0lexltpi =(x)...

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  4. If f(x)=2x-1, " if " x gt1, =x^(2)+1," if " -1 le xle1," then "(f(1)...

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  5. If f(x)=4x-1," if " x gt4, =x^(2)-2," if " -2 le x le 3, =3x+4," i...

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  6. If f(x)=(cos^(2)x+sin^(4)x)/(sin^(2)x+cos^(4)x) for x in R then f(2002...

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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)=alphax+beta and f={(1, 1), (2, 3), (3, 5), (4, 7)} then the va...

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  9. If f: R rarrR defined by f(x)=2x+|x| then f(3x)-f(-x)-4x=

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  10. If f:R rarrR is defined by f(x)=2x+|x| then f(2x)+f(-x)-f(x)=

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  11. If f(1)=1, f(n+1)=2f(n)+1, n ge1, then f(n) is

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  12. If f(x)=log.(1+x)/(1-x) then f((x(1)+x(2))/(1+x(1)x(2)))=

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

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

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

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

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

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

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

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  20. 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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