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Express each of 1+x+x^2 function as the ...

Express each of `1+x+x^2` function as the sum of an even function and an odd function.

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MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Find the composition fog and gof and test whether fog = gof when f and...

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  2. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

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  3. Express each of 1+x+x^2 function as the sum of an even function and an...

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  4. Express each of x^2 function as the sum of an even function and an odd...

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  5. Express each of e^x function as the sum of an even function and an odd...

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  6. Express each of e^x+ sin x function as the sum of an even function and...

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  7. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  8. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  9. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  10. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  11. Let X ={1,2,3,4}Determine whether f:X rarr Xdefined as given below hav...

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  12. Construct an example to show that f(A nn B )!= f(A) nn f(B) where A nn...

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  13. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  14. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

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  15. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

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  16. Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A n...

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  17. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

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  18. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  19. Determine whether a ** b = 2a +3b "on" Z operations as defined by * a...

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  20. Determine whether a** b =ma - nb "on" Q + "where" m "and" n in N ope...

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