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If f(x) and g(x) be two given function w...

If f(x) and g(x) be two given function with all real numbers as their domain, then `h(x)={f(x)+f(-x)}{g(x)-g(-x)}` is

A

an even function

B

an odd function

C

even as well as odd function

D

None of these

Text Solution

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The correct Answer is:
B
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PATHFINDER-FUNCTION-QUESTION BANK
  1. If f is even function defined on the interval (-5, 5), then real value...

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  2. Which of the following function is even function

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  3. If f(x) and g(x) be two given function with all real numbers as their ...

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  4. Period of f(x)=[x]+[x+1/3]+[x+2/3]-3x+10, where [.] denotes the greate...

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  5. The function f(x)=1/2{|sin x|/cos x +sin x/|cos x|} is periodic with p...

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  6. The value of n in 1, for which the function f(x)=(sin nx)/(sin frac xn...

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  7. If f(x) = is an odd periodic function with period 2, then f(4) equals

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  8. Period of f(x)=cos2pi{x} is , where {x} denote the fractional part of ...

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  9. The period of sin((pi{x})/12)+cos((pi x)/8)+tan((pi{x})/3)

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  10. Let f : (4, 6)to(6, 8) be a function defined by f(x) x+[x/2] (where [....

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  11. The value of b and c for which the identity f(x+1)-f(x)=8x+3 is satisf...

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  12. If f(x)=sin sqrt([a])x, (where [.] denotes the greatest integer functi...

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  13. If f : R to [-1, 1], where f(x)=sin(pi/2[x]) (where [.] denotes the gr...

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  14. If [x]^2-5[x]+6=0 (where [.] denotes the greatest integer function), t...

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  15. Let f:(-infty,1]to(-infty,1] such that f(x)=x(2-x). Then f^(-1)(x)

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  16. Let f : R to R be a function such that f(x)=x^3+x^2+3x+sinx . Then

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  17. Let f:[-pi/3,(2pi)/3]to[0,4] be a function defined as f(x)=sqrt3sinx-c...

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  18. Let f(x) = (ax+b) cos x+ (cx+ d) sin x and f' (x) = x cos x be an iden...

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  19. If f(x)=cos |x|+[|sin x/2|] (where [.] denotes the greatest integer fu...

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  20. The number of points (x, y), where the curves |y| = In|x| and (x-1)^2+...

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