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If f(x) + g(x) = e^(-x) where f(x) is a...

If `f(x) + g(x) = e^(-x)` where f(x) is an even function and g(x) is an odd function then `f(x)`=

A

`e^(-x)/2`

B

`(e^(x) + e^(-x))/2`

C

`(e^(x)-e^(-x))/2`

D

`e^(x)/2`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-FUNCTIONS -EXERCISE -II
  1. f{x) is an even polynomial function. Then sin(f(x)-3x) is

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

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

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

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

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

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

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

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

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

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  11. If f: R to R is defined by f(x) =x-[x], then the inverse function f^(-...

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  12. Suppose f(x) =(x+1)^(2) for x ge -1. If g(x) is the function whose gr...

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  13. Let f(x) =(x+1)^2-1,x ge -1 then {x: f(x) =f^(-1)(x) } =

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  14. {x in RR:(2x-1)/(x^(3)+4x^(2)+3x) in RR}=

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  15. The domain of (1)/(sqrt(x-x^(2)))+sqrt(3x-1-2x^(2)) is

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  16. Domain of the real valued function: sqrt(25-9x^(2)) + sqrt(x^(2) + x...

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  17. The domain of f(x) = sqrt((x-3)/(x+3)) + sqrt((2-x)/(2+x)) is

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  18. The domain of f(x) =1/sqrt((x-1)(x-2)(x-3)) is

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  19. The domaini of sqrt((2x+1)/(2x^(3) + 3x^(2) +x)) is:

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  20. The domain of the function f(x)=sqrt([(2x-1)/(x^(2)-10x-11)]) is

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