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Let R be the set of all real numbers ...

Let R be the set of all real numbers let `f: R to R : f(x) = sin x ` and
`g : R to R : g (x) =x^(2) .` Prove that g o f `ne ` f o g

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ML KHANNA-CONCEPTS OF SET THEORY -Problem Set (3) (FUNCTIONS AND MAPPING)
  1. If the mapping f and g are given by f = {(1, 2), (3, 5), (4, 1)} a...

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  2. If the functions f:RrarrRandg:RrarrR be defined by f(x)=2x+1,g(x)=x^(2...

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  3. Let R be the set of all real numbers let f: R to R : f(x) = sin x ...

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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. Given f(x)=log(10)((1+x)/(1-x)) and g(x)=(3x+x^(3))/(1+3x^(2)), then f...

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

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

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

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

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

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

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

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

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

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

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

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

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

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