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Let f : W rarr W be defined as f (x) = x...

Let f : W `rarr` W be defined as f (x) = x -1 if x is odd and f(x) = x +1 if x is even then show that f is invertible. Find the inverse of f where W is the set of all whole numbers.

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MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  2. Prove that the acute angle between the lines whose direction cosines a...

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  3. Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...

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  4. Constract the composition table/multiplication table for the binary op...

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  5. Let A = ( ( 1 2 2) , (2 1 2), (2 2 1)).Find A^-1 and hence show A^2-4A...

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  6. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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  7. Show that the sum of the intercepts on the coordinate axes of any tang...

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  8. Shows that the triangle of greatest area that can be inscribed in a ci...

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  9. Find the area of the région on closed between y = 4x-1 and y^2=2x

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  10. Write fog if f:R rarr R and g: R rarr R is given by f(x) = | x| and g(...

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  11. Evaluate : tan^(-1)((-1)/sqrt3)+cot^(-1)(1/sqrt3)+tan^(-1)(sin(-π/2)).

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  12. If | adj A | = 64 then find | A |

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  13. Evaluate the following : [[sin^2theta,cos^2theta,1],[cos^2theta,sin^2t...

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  14. A differentiable function f defined for all x > 0 and satisfies f(x^2)...

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  15. Write the minimum value of y2 where y=sin^2x cos^2x

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  16. Evaluate int-1^1e^|x| dx

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  17. Write the vector equation ofthe plane whose cartesian equation is x + ...

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  18. Let A (1,2,3). Then, find the number of equivalence relations containi...

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  19. Let f ,g: R rarr R be two functions defined as f(x) = |x| +x and g(x) ...

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  20. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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