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Show that any function can be expressed as the sum of an odd function and even function

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Prove that every function can be expressed as the sum of an -even and an odd function.

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Prove that the derivative of an odd function an ever function .

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The derivative of an odd function is always

Prove that the sum of two odd numbers is even.

f(x)=(cosx)/([(2x)/pi]+1/2), where x is not an integral multiple of pi and [dot] denotes the greatest integer function, is an odd function an even function neither odd nor even none of these

f(x)= cosx/([2x/pi]+1/2) where x is not an integral multiple of pi and [ . ] denotes the greatest integer function, is (a)an odd function (b)an even function (c)neither odd nor even (d)none of these

The function f(x)=(x+1)/(x^3+1) can be written as the sum of an even function g(x) and an odd function h(x) . Then the value of |g(0)| is___________

Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then f(x) is an odd function f(x) is a one-one function f(x) is an onto function f(x) is an even function

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If p and q are positive integers, f is a function defined for positive...

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  2. Each question has four choices, a,b,c and d,out of which only one is ...

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  3. Show that any function can be expressed as the sum of an odd function ...

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  4. Each question has four choices, a,b,c and d,out of which only one is ...

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  5. Each question has four choices, a,b,c and d,out of which only one is ...

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  6. Let f(x)=log2 log3log4log5(sin x+a^2). Find the set of values of a for...

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  7. Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2...

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  8. If fa n dg are two distinct linear functions defined on R such that th...

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  9. Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that ...

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  10. Let f:XtoY be a function defined by f(x)=asin(x+pi/4)+bcosx+c. If f is...

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  11. If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx ...

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  12. Let R="{"x , y")": x , y in R ,x^2+y^2lt=25}andR^(prime)={(x , y): x ...

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  13. A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c le...

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  14. The period of the function f(x)=[6x+7]+cospix-6x , where [dot] denotes...

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  15. If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetric ab...

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  16. The solution set for [x]{x}=1 (where {x} and [x] are respectively, fr...

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  17. Let f: RvecR be a continuous and differentiable function such that (f(...

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  18. The possible values of a such that the equation x^2+2a x+a=sqrt(a^2+x-...

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  19. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

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  20. Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] den...

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