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Show that f: N->N defined by f(n)={(n+1)...

Show that `f: N->N` defined by `f(n)={(n+1)/2,\ \ if\ n\ i s\ od d n/2,\ if\ n\ i s\ e v e n` is many-one onto function.

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Show that f:n rarr N defined by f(n)={(((n+1)/(2),( if nisodd)),((n)/(2),( if niseven )) is many -one onto function

Let f: NvecN be defined by f(n)={(n+1)/2, "if" n "i s o d d"n/2, "if "n "i s e v e n" for a l l n N} Find whether the function f is bijective.

Show that f : NvecN , given by f(x)={x+, if x i s od dx-1, if x i s e v e n is both one-one and onto.

Let f:N->N be defined as f(n)= (n+1)/2 if n is odd and f(n)=n/2 if n is even for all ninN State whether the function f is bijective. Justify your answer

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

Let f: Z->Z be given by f(x)={x/2,\ if\ x\ i s\ e v e n,0,\ if\ x\ i s\ od d . Then, f is (a) onto but not one-one (b) one-one but not onto (c) one-one and onto (d) neither one-one nor onto

Let f:N rarr N be defined by: f(n)={n+1,quad if n is oddn -1,quad if n is even Show that f is a bijection.

Let f" ": N->N be defined by f(n)={(n+1)/2,""if""""n""""i s""""odd" " n/2,""if""""n""""i s""e v e n for all n in N . State whether the function f is bijective. Justify your answer.

MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Exercise 2(c )
  1. (i) If f(x) = 3x^(4)- 5x^(2) + 7, " find " f(x-1) (ii) If f(x) = x^(...

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  2. (i) If f(x) = x + (1)/(x) prove that: [f(x)]^(3) = f(x^(3)) + 3f ((1...

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  3. (i) If y = f(x) = (3x-1)/(5x-3), prove that f(y) = x (ii) If y = f(x...

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  4. If f(x) = log(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to...

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  5. (a) What are the real numbers x such that [x] =2? (b) What are the v...

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  6. What values does the function x rarr 2x^(2)-1 associate with the numbe...

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  7. Given f(x) = {(3x-8" for " ,x le5),(7 " for " ,x gt 5):} What is the...

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  8. What is the domain of the function (x)/(x^(2) - 3x + 2) ?

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  9. What is the range of the constant function 1 ?

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  10. For what values of x are the following functions not defined ? (i) (3x...

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  11. Find the periods of the following functions, if periodic : (i) | cos x...

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  12. Show that f: N->N defined by f(n)={(n+1)/2,\ \ if\ n\ i s\ od d n/2,\ ...

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  13. If f(x)=cos(logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

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  14. (1) If f(x) = sqrt(x), prove that : (f(x + h) - f(x))/(h) = (1)/(sq...

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  15. Find domain(i) f(x) = (1)/(x - 5) (ii) f(x) = (3 - x)/(x - 3) (iii) f(...

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  16. (i) f(x) = sqrt(3 - 2x) (ii) f(x) = (1)/(sqrt(x + 2)) (iii) f(x) =...

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  17. Find the domain of f(x) = sqrt(log((5x - x^(2))/(6))

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  18. State, given justification for your answer, which of the following pai...

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  19. Are the following functions invertible in their respective domains ? I...

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  20. Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and he...

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