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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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The correct Answer is:
`f^(-1) (x) = {{:(x+1,"if x is even"),(x-1,"if x is odd"):}`
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ARIHANT PRAKASHAN-SIMILAR TEST 3 -SECTION B
  1. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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

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  3. Solve for x , tan^(-1) x+2 cot^(-1) x = (2pi)/3

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  4. Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+...

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  5. Solve the following LPP graphically Minimise Z = 5x+10 y Subject ...

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  6. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  7. Show that the following system is inconsistent. (a-b)x+(b-c)y+(c-a)z...

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  8. If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .

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  9. On a multiple choice examination with three possible options for each ...

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  10. An instructor has a question bank consisting of 300 easy true/false qu...

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  11. If y = log (x+sqrt(1+x^(2))) , then find y(2)(0).

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  12. Differentiate the following function w.r.t. x, (logx)^(x)+x^(logx).

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  13. Find the equation of normal to the curve y = e^(sin x) " at "x = pi...

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  14. Find the approximate value of f(2.01), where f(x) = 4x^(2) + 5x+2

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  15. Discuss the continuity of the function f(x) at x=1/2 , when f(x) is de...

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  16. Integrate int cot^(-1) x dx.

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  17. Integrate int sqrt (7x-10 -x^(2)) dx

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  18. Evaluate int(0)^(pi) |cos x |dx.

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  19. Find the area bounded by y = |x-1| and y=1 .

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  20. Solve (dy)/(dx) +(sec x) y = tan x.

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