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Examinef: R rarr R, f(x) ="sgn" x functi...

Examine`f: R rarr R, f(x) ="sgn" x` functions if it is (i) injective (ii) surjective, (iii) bijective and (iv) none of the three.

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MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Examine f:R rarr R, f(x) = [x] ="the greatest integer" le x. function...

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

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

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

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  5. Show that f(x)=sin x on [0, pi/2] functions are injective.

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

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

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  8. Show that f(x)=a^x "on" R.(a gt 0 "and" a != 1) functions are injectiv...

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

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

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  11. Give an example of a function which is injective but not surjective.

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  12. Give an example of a function which is neither injective nor surjectiv...

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  13. Give an example of a function which is bijective

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  14. Prove that {1,2,3,4,5,6,……} set are equivalent.

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

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

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

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

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  20. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

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