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Show that the function f:R rarr R given ...

Show that the function `f:R rarr R` given by `f(x)=x^3` is injective.

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Show that the function f:RrarrR given by f(x)=x+x^3 is a bijective function.

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Prove that the function f: R rarr R given by f(x)=2 x is one-one and onto.

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Show that the function f : R_** rarr R_** defined by f (x) = 1/x is one-one and onto,where R_** is the set of all non-zero real numbers. Is the result true, if the domain R_** is replaced by N with co-domain being same as R_** ?

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Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q (the set of all rational numbers) is a bijection.

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V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

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  2. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 i...

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  3. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

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  4. Show that the function f:R rarr R given by f(x)=x^3 is injective.

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  5. Given a non empty set X, consider P(X) which is the set of all subsets...

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  6. Find the number of all onto functions from the set {1,2,3 …... n}to i...

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  7. Let S={a, b, c} and T={1,2,3}, Find F^-1 of the following functions F ...

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  8. Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions define...

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  9. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)20 ...

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  10. Show that the relation R on the set N xx N defined by (a, b)R(c, d)...

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  11. If f: R rarr R be a function defined by f(x)=4 x^3-7, show that the fu...

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  12. Consider the binary operation ast : QtoQ where Q is the set of rationa...

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  13. Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q...

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  14. Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-...

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  15. Let f: R rarr R be a function defined by f(x)=x^2-3 x+2 Find f^' (2) a...

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  16. If f : R rarrR be defined by f(x) = 5x - 3, then prove that f is one-o...

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  17. Let f, g: R rarr R be defined by f(x)=x^2+1and g(x)=sin x. Find f o g ...

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  18. If f, g: R rarr R are defined by f(x)=x^2+3 x+1, g(x)=2 x-3, find (i) ...

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  19. Let * be a binary operation on N, the set of all natural numbers defin...

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  20. Let A=N xx N and let * be a binary operation on A defined by (a, b)*(...

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