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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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MODERN PUBLICATION-TEST PAPER 7-EXERCISE
  1. Write the parameteric equation of a line through parallel to the vecto...

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  2. If alphahati +3hatj -hatk and 2hati + hatj-1/3hatk are parallel then ...

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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. Given a non-empty set X, Let *: P(x) xx P(x) be defined as A**B =(A-B...

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  5. Let R be a relation on the set A of ordered pairs of positive integers...

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  6. Let R be the relation on the set R of real numbers such that aRb iff a...

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  7. An animal feed company must produce 200kg of a mixture consisting of i...

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  8. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

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  9. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  10. Express as a sum of a symmetric and a skew symmetric matrix: [[x,a,b],...

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  11. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

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  12. Test differentiability of the following function at the indicated poin...

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  13. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  14. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  15. If tangents are drawn from the origin to the curve y = sin x then sho...

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  16. Test the function y = (x - 5)^5( x + 2)^2 for extreme values.

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  17. Evaluate : int ((sinxcosx)/(sin2x) - 2sinx+3)dx .

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  18. int0^(pi/2)(cosxdx)/((sinx+1)(sinx+2))

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  19. Solve : (x + 2y^3)dy/dx = y.

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  20. Find the general solution of dy/(du) = u+1/sqrtu + 6u + 5.

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