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If A = R -{3} and B = R -{1}. Consider t...

If A = R -{3} and B = R -{1}. Consider the function `f:A to B` defined by `f(x)=(x-2)/(x-3)`, for all `x in A`. Then, show that f is bijective. Find `f^(-1)(x)`.

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SHARAM PUBLICATION-MODEL QUESTION PAPER 20-EXERCISE
  1. Solve(x log x )dy/dx+y=2 log x.

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  2. Show that the relation R defined on the set Z of all integers defined ...

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  3. If A = R -{3} and B = R -{1}. Consider the function f:A to B defined b...

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  4. Prove that 2 tan^-1(1/2) + tan^-1 (1/7) = tan^-1 (31/17).

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  5. Find the feasible region of the system. 2y-xge0,6y-3xle21,xge0,yge0

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  6. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  7. The diagonals of a parallelogram are given by veca =2hati - 3hatj + 5h...

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  8. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

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  9. Find the equation of planes passing throught the points (1,2,3),(1,-4,...

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  10. Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y ...

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  11. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

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  12. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  13. Solve the LPP Maximize z=5x+3y Subject to 3x+5yle15 5x+2yle10 , ...

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  14. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

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  15. If a, b and c are all positive real, then prove that minimum value of ...

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  16. Find the value of k so that the function f defined by f(x)={((kcos x)/...

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  17. If y = x^(cotx) then find (dy)/(dx).

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  18. Show that the rectangle of maximum area that can be inscribed in a giv...

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  19. Evaluate int0^ pi x/(1+ sin x) dx

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  20. Find the area of region in the first quadrant enclosed by the X-axis, ...

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