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Determine if each function given below i...

Determine if each function given below is one-to-one
(i) To each state of India assign its capital.
(ii) To each person on earth assign the number, which corresponds to his height.
(iii) To each country in the world assign the latitude and longitude of its capital.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Exercise 2(c )
  1. Which of the following relations are functions? Give reasons. If it is...

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  2. Determine if each function given below is one-to-one (i) To each sta...

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  3. If f: A->B is an injection such that range of f={a} . Determine the...

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  4. (i) If f(x) = 3x^(4)- 5x^(2) + 7, " find " f(x-1) (ii) If f(x) = x^(...

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  5. (i) If f(x) = x + (1)/(x) prove that: [f(x)]^(3) = f(x^(3)) + 3f ((1...

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  6. (i) If y = f(x) = (3x-1)/(5x-3), prove that f(y) = x (ii) If y = f(x...

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  7. If f(x) = log(e) ((1-x)/(1+x)) , then f((2x)/(1 + x^(2))) is equal to...

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  8. (a) What are the real numbers x such that [x] =2? (b) What are the v...

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  9. What values does the function x rarr 2x^(2)-1 associate with the numbe...

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  10. Given f(x) = {(3x-8" for " ,x le5),(7 " for " ,x gt 5):} What is the...

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  11. What is the domain of the function (x)/(x^(2) - 3x + 2) ?

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  12. What is the range of the constant function 1 ?

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  13. For what values of x are the following functions not defined ? (i) (3x...

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  14. Find the periods of the following functions, if periodic : (i) | cos x...

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  15. Show that f: N->N defined by f(n)={(n+1)/2,\ \ if\ n\ i s\ od d n/2,\ ...

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  16. If f(x)=cos(logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

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  17. (1) If f(x) = sqrt(x), prove that : (f(x + h) - f(x))/(h) = (1)/(sq...

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  18. Find domain(i) f(x) = (1)/(x - 5) (ii) f(x) = (3 - x)/(x - 3) (iii) f(...

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  19. (i) f(x) = sqrt(3 - 2x) (ii) f(x) = (1)/(sqrt(x + 2)) (iii) f(x) =...

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  20. Find the domain of f(x) = sqrt(log((5x - x^(2))/(6))

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