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Let A = R-{2} and B = R - {1}. If f : A ...

Let A = R-{2} and B = R - {1}. If f : A `rarr` B is a function defined by f(x)= `(x-1)/(x-2)` then show that f is one-one and onto. Hence, find `f^(-1)`.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 7-Section B (60 MARKS)
  1. One kind of cake requires 200 g of flour and 25 g of fat and another k...

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  2. Let * be a binary operation on Q defined by a**b=ab+1. Determine wheth...

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  3. Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined b...

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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. There are 25 tickets bearing numbers from 1 to 25. One ticket is drawn...

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  6. IF A=[(1,tanx),(-tanx,1):}] then show that A^TA^-1=[(cos2x,-sin2x),(s...

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  7. Show that the following systems of linear equations is consistent and ...

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  8. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  9. Find the probability distribution of number of doublets in four throws...

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  10. Find the equasion of the tangents drawn from the point (1,2) to the cu...

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  11. Find the intervals in which the function y="sin"x,x in[0, 2pi] is in...

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  12. If y =(sin^(-1) x)^2, prove that (1-x^2)y2 - xy1 - 2 = 0

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  13. Differentiate "log"(10)x+"log"(x)10+"log"(x)x+"log"(10)10.

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  14. Verify the LMVT for the function f(x)=(1)/(4x-1),1lexle4.

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  15. Find the solution of the differential equation. (x-y-2)dx+(x-2y-3)dy...

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  16. Find the differential equation by eleminating the orbitary constants i...

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  17. Evaluate the following integrals : int(e^(6logx)-e^(5logx))/(e^(4log...

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  18. Prove that int(-1)^(1)log((2-x)/(2+x))dx=0

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  19. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

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  20. By computing shortest distance, determine whether the following pair o...

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