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Let X ={x,y} and Y ={u,v}. Write down al...

Let X ={x,y} and Y ={u,v}. Write down all the functions that can be defined from X To Y. How many of these are (i) one-one (ii) onto and (iii)one-one and onto ?

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ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS ( Exercise 1 (b))
  1. Let X ={x,y} and Y ={u,v}. Write down all the functions that can be de...

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  2. Let X and Y be sets containing m and n elements respectively. (i) Wh...

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  3. Examine f :R rarr R, f(x) =x^2functions if it is (i) injective (ii) s...

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  4. Examine f:R rarr [-1,1],f(x) = sin x functions if it is (i) injectiv...

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  5. Examine f:R+ rarr R +, f(x) =x +1/x "where"R+={x in R :x gt 0} functi...

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  6. Examinef:R rarr R ,f(x) =x^3 +1 functions if it is (i) injective (ii)...

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  7. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

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  8. Examine f:R rarr R, f(x) = [x] ="the greatest integer" le x. function...

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  9. Examine f:R rarr R, f(x) =|x| functions if it is (i) injective (ii) s...

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  10. Examinef: R rarr R, f(x) ="sgn" x functions if it is (i) injective (i...

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  11. Examine f:R rarr R, f = id R="the identity function or R."functions i...

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  12. Show that the functions are injective f(x) = sinx on [ 0, (pi)/(2)...

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  13. Show thatf(x)= cos x [0 , pi] functions are injective.

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  14. Show that f(x) = loga x "on" (0,oo ),(a gt 0 "and" a != 1) functions a...

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  15. Show that the function f(x)=a^(x), x in R is injective, where (a gt 0 ...

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  16. Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 a...

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  17. Give an example of a function which is Surjective but not injective.

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  18. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  19. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  20. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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