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Show that f\ : NvecN ,\ given by f(x)=...

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

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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: 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

Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

Show that f: R->R , given by f(x)=x-[x] , is neither one-one nor onto.

A function f from the set of natural numbers to integers defined by f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d-n/2,\ w h e n\ n\ i s\ e v e n is (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

Show that the function f: N->N , given by f(x)=2x , is one-one but not onto.

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.

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1,\ if\ n\ i s\ od d Show that f is a bijection.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value o...

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  2. Find the particular solution of the differential equation. (dy)/(dx...

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  3. Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od d \ \ x-...

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  4. Evaluate : int(logx)/x\ dxdot

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  5. What is the value of the determinant |(0,2,0),(2,3,4),(4,5,6)|?

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  6. What is the degree of the following differential equation? 5x\ ((d...

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  7. What is the range of the function f(x)=(|x-1|)/((x-1))?

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  8. If A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]], then for what val...

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  9. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

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  10. Find the equation of the plane through the points (2, 1, 1) and (1, ...

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  11. Find the shortest distance between the following lines: (x+1)/7=(y+1)...

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  12. A cottage industry manufactures pedestal lamps and wooden shades, e...

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  13. A factory has two machines A and B. Past record shows that machine A...

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  14. Find the inverse of the following matrix using elementary operations: ...

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  15. Using properties of determinants, prove the following: |[x,x^2,1+px^3]...

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  16. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

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  17. Solve the following for x : cos^(-1)((x^2 - 1)/(x^2 + 1))+t a n^(-1...

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  18. Using matrices, solve the following system of equations: x\ -\ y+z...

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  19. If A^(-1) =[(3,-1,1),(-15,6,-5),(5,-2,2)] and B = [(1,2,-2), (-1,3,0),...

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  20. A merchant plans to sell two types of personal computers - a deskto...

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