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If R is a set of real numbers and f :R t...

If R is a set of real numbers and f :`R to R ` is given by the relation f (x) = sin x, ` x in R` and mapping g: `R to R` by the relation `g(x)= x^2 , X in R`, then prove that `f o g ne g o f.`

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ML KHANNA-FUNCTIONS-PROBLEM SET (2)
  1. If the mappings f and g are given by f = {(1,2),(3,5),(4, 1)}, g= {(2,...

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  2. If the functions f:R to R and g: R to R be defined by f (x) = 2x+1, g...

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  3. If R is a set of real numbers and f :R to R is given by the relation ...

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  4. Let f:R to R, g: R to R be two functions given by f(x)=2x-3,g(x)=x^(3)...

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  5. If f(x) = (3x +2)/(5x -3) then

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  6. Let f : R rarr R be defined by f(x) = cos (5x+2). Is f invertible? Jus...

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  7. A mapping is defined as f:R to R. f (x) = cos x. Show that it is neit...

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  8. Let C be the set of complex numbers. Prove that the mapping f: C to R...

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  9. Let A=R-{3},B=R-{1} " and " f:A rarr B defined by f(x)=(x-2)/(x-3). Is...

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  10. Let f: R to R be defined by f(x) = 3x + 4, X in R Is f invertible ? ...

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  11. The composite mapping fog, of the maps f: R to R, f (x)=sin x, g : R ...

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  12. Let A and B be two sets with a finite number of elements. Assume that ...

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  13. If f: R to R is defined by f (x)= x^2 + 1, then values of f^(-1) (17) ...

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  14. Which of the statements given below is different from the other?

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  15. Find the domain and range of f (x)= x^2 //(1+x^2)(x real). Is the func...

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  16. If A={x:-1 le x le 1} = B. Discuss the following functions w.r.t. one...

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  17. Set A has 3 elements and set B has 4 elements. The number of injection...

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  18. The number of surjections from A={1,2,... n}, n ge 2, onto B = {a,b} ...

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  19. Let A and B be two finite sets having m and n elements respectively. T...

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  20. The total number of injective mappings from a set with melements to a ...

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