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State with reason whether the following ...

State with reason whether the following functions have inverse
f : {1,2,3,4} to {10} with
f = {(1,10),(2,10),(3,10),(4,10)}

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Find f o g and g o f f(x) = |x| and g(x) = |5x -2|

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  2. If f(x) =(4x + 3)/(6x - 4), x ne 2/3, show that (fof)(x) = x, for all ...

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  3. State with reason whether the following functions have inverse f : {...

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  4. Show that f:[-1,1]toR given by f(x)=frac(x)(x+2) is one-one.

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  5. Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. ...

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  6. Consider f:R^+to[-5, infty) given by f(x)=9x^2+6x-5. Show that f is ...

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  7. Let f : X rarr Y be invertible, show that f has unique inverse

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  8. Consider f : {1, 2, 3} rarr {a, b, c} given by f(1) = a, f(2) = b and ...

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  9. Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, ...

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  10. If f : R rarr R be given by f(x) = (3 - x^3)^(1/3), then (f o f) (x) i...

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  11. f : R - {(-4)/3} rarr R be a function defined as f(x) = (4x)/(3x +4). ...

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  12. Can you define a function from 'RxR rarr R' such as 'f3: RxR rarr, R' ...

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  13. Can yóu define a function from 'R xx R rarr R' such as 'f4: R xx R rar...

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  14. Show that addition, subtraction and multiplication are binary opera...

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  15. Show that subtraction and division are not binary operations on N.

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  16. Show that *: R xx R rarr R is given by (a, b) rarr(a+4 b)^2 is a binar...

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  17. Let P be the set of all subsets of a given set X. Show that uu: P xx P...

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  18. Show that the vee: R xx R rarr R given by (a, b) rarr max {a, b} and t...

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  19. Show that +: R xx R rarr R and xx: R xx R rarr R are commutative binar...

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  20. Show that *: R xx R rarr R defined by a * b=a+2 b is not commutative.

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