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Prove that the product of two odd functi...

Prove that the product of two odd functions is an even function while their sum is an odd function.

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Prove that the product of two even or two odd functions is an even function, whereas the product of an even and an odd function is an odd function.

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Odd & Even Function

Even and Odd Function

A DAS GUPTA-Function-Exercise
  1. Find the domain and range of the followingf(x)=1/(3-cos2x)

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  2. Let f : {x,y, z} to {a, b, c} be a one-one function. If it is known th...

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  3. Prove that the product of two odd functions is an even function while ...

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  4. Prove that f(x)=root(3)(1-(x)^2+root(3)(1+(x)^2) is an even function

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  5. Extend f(x)=x^2+x defined in [0,3] onto the interval[-3,3] so that f(x...

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  6. Period of |sinx+cosx| is

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  7. If f(x) in [1,2] where x in R and for a fixed positive real number p, ...

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  8. Let f (x ) and g(x) be increasing and decreasing functions respectivel...

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  9. Computer the inverse of the function : f(x) = (x + sqrt(x^(2) + 1))

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  10. If f(x)=1-x/(1+x), x not equal to -1 then f{f(1/x)}=

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  11. If f(x)=cos(logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

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  12. If f(x)=(x+1)/x and phi(x)=(x^4+1)/(x^4) then phi(a)=-- where f(a)=5.

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  13. If f(x) is a polynomial function of the second degree such tha f(0)=5,...

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  14. If f(x+1)=x^(2)-3x+2 then f(x) is equal to

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  15. If f is an even function defined on the interval (-5,5), then four rea...

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  16. If f(x) is a periodic function of the period k then f(ax+b) is a perio...

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  17. The value of f(x)=3sin((pi^2)/(16)-x^2) lie in the interval

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  18. If f:RrarrR be a function given f(x)=sqrt1- sqrt(1-x^2) then the domai...

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  19. If the function f : [2,+prop)rarrX be bijective wheras f(x)= 5-4x+x^2 ...

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  20. Find the domain f(x)=log(100x)((2 log(10) x+1)/-x)

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