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A mapping is defined as f:R to R. f (x)...

A mapping is defined as f:`R to R`. f (x) = cos x. Show that it is neither one-one nor surjective.

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ML KHANNA-CONCEPTS OF SET THEORY -Problem Set (3) (FUNCTIONS AND MAPPING)
  1. Given f(x)=log(10)((1+x)/(1-x)) and g(x)=(3x+x^(3))/(1+3x^(2)), then f...

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  2. Let f:RrarrR be defined by f(x)="cos"(5x+2). If f invertible ?

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

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

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

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

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

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

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

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

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  12. If A={x:-1lexle1} and f be a function on A. Discuss the following func...

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  13. If A={x:-1lexle1}=B. Discuss the following functions w.r.t. one-one-on...

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  14. Let f:AtoA where A={x:-1lexle1}. Find whether the following function a...

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  15. If f :A-> A,A={x:-1lexle1}=B. Discuss the following functions w.r.t. o...

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  16. If f :A-> A,A={x:-1lexle1}=B. Discuss the following functions w.r.t. o...

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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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