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Prove that Modulus Function f: R rarr R ...

Prove that Modulus Function `f: R rarr R` given by : `f(x) = | x |` is neither one-one nor onto, where `| x |` is x, if x is positive and `| x |` is - x, if x is negative.

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MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Check the injectivity and surjectivity of the following function: f ...

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  2. Prove that greatest integer function f: RrarrR, given by f (x) = [x], ...

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  3. Prove that Modulus Function f: R rarr R given by : f(x) = | x | is nei...

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  4. Show that the signum function f : R to R given by: f(x) = {{:(1, if ...

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  5. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6...

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  6. In the following case, state whether the function is one-one, onto or ...

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  7. Let A and B be sets, show that f : A xx B rarr B xx A such that f(a,b...

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  8. Let f: N to N be defined by f(n) = {{:((n+1)/2, " if n is odd "),(n/2,...

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  9. Let A =R-{3} and B=R-{1}. Consider the function f : A to B defined by ...

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  10. Let f : R rarr R be defined as f(x) = x^4. Choose the correct answer.

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  11. Let f : RrarrR be defined as f (x) = 3x Choose the correct answer.

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  12. If f:(1,3,4} rarr {1, 2,5} and g:(1,2,5) {1,3} be given by f = {(1, 2)...

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  13. Let f,g and h be function from R to R. Show that (f+g) o h = foh + goh

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  14. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

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  15. Find gof and fog, if f(x) = 8x^3 and g(x) = x^(1/3)

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

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  17. State with reason whether following functions have inverse: h: {2,3,4,...

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  18. State with reason whether following functions have inverse: g: {5,6,7,...

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  19. State with reason whether following functions have inverse: h: {2,3,4,...

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  20. Show that f: [ -1, 1] rarr R, given by f(x)= (x)/(x+2) is one-one. Fin...

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