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Prove that the relation R in Z of intege...

Prove that the relation R in Z of integers given by: `R = {(x, y): 2x - 2y` is an integer } is an equivalence relation. [3] If `f: RrarrR` defined by `f(x) = (4- 3x)/5` is an invertible function, find `f^-1`.

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BETTER CHOICE PUBLICATION-RELATIONS AND FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Find fog and gof , if f(x) = x^2 , g (x) = x +1

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  2. If f :Rrarr R defined by f(x)= (5x+6)/7 is an invertible function, ...

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  3. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

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  4. Prove that the relation R in Z of integers given by: R = {(x, y): 3x -...

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  5. Show that the relation R defined by R = {(a, b) (a - b), is divisible ...

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  6. Check the injectivity and surjectivity of the following function: f ...

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  7. Check the injectivity and surjectivity of the following function: f :...

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  8. If f(x) =x/(x-1) then show that (fof)(x) = x.

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  9. If f:(1,3,4} rarr {1, 2,5} and g:(1,2,5) {1,3} be given by f = {(1, 2)...

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  10. If f : R rarr R defined by : f(x) = frac {3-2x}{4} is an inversible fu...

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  11. If f : R rarr R defined by : f(x) = frac {6-5x}{7} is an inversible fu...

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  12. Prove that the relation R in Z of integers given by: R = {(x, y): 2x -...

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  13. Let f:NrarrY, be a function defined as f(x) = 4x+3, where, Y = {y in ...

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  14. In a binary operation **: phi xx phi rarr phi is defined as a ** b = (...

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  15. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

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  16. If f(x) = 4x – 1 and g(x)=x^3 + 2, find gof

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  17. If f(x) = sin x and g(x) = 2x, find fog.

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  18. Is f(x) = (x-1)/(x+1) invertible in its domain ? If so find, f^(-1) F...

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  19. Consider f:R^(+) rarr [-5, oo] given by f (x) = 9x^(2) + 6x - 5 show ...

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  20. If a**b=a/2+b/3 then find value of 2 ** 3.

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