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If functions f:A to B and g : B to A sat...

If functions `f:A to B` and `g : B to A` satisfy `gof= I_(A),` then show that `f` is one-one and g is onto.

A

f is one-one

B

g is one-one

C

f and g both are one-one

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Exercise
  1. If f:R->R be defined by f(x)=x^2+1, then find f^(-1)(17) and f^(-1)(-3...

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  2. The function f: NvecN(N is the set of natural numbers) defined by f(n)...

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

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  4. If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

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  5. f : R rarr R is a function defined by f (x) = 10 x - 7. If g = f^(-1),...

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  6. Let A={x in R : xlt=1} and f: A->A be defined as f(x)=x(2-x) . Then, ...

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  7. If f(x)=x^n , n in Nandgof(x)=ng(x) then g(x) can be

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  8. If the function f: R->R be such that f(x)=x-[x] , where [x] denotes th...

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  9. f:R to R given by f(x)=5-3 sin x, is

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  10. Let f:A->B be a function defined by f(x) =sqrt3sin x +cos x+4. If f is...

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  11. Let f: A to B; g: B to A be two functions such that gof = IA. Then; f ...

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  12. Let f: A to B; g: B to A be two functions such that fog = IB. Then; f ...

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  13. If f: A->B and g: B->C are one-one functions, show that gof is one-o...

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  14. If functions f:A to B and g : B to A satisfy gof= I(A), then show that...

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  15. Suppose f:A to B " and " B to C. (i) Prove that if f is onto and g i...

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  16. If f: A->B and g: B->C are one-one functions, show that gof is one-o...

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  17. Let [x] denote the greatest integer less than or equal to x . If f(x...

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  18. If f(x)=sin^(2)x, g(x)=sqrtx and h(x)=cos^(-1)x, 0 le xle 1, then

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  19. If f(x)=(25-x^(4))^(1//4)"for "0 lt x lt sqrt5, "then"f(f((1)/(2)))=

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  20. If X={1,2,3,4}, then one-one onto mappings f:X to X such that f(1)=1, ...

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