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Consider functions f and g such that com...

Consider functions f and g such that composite gof is defined and is one-one.Are f and g both necessarily one-one.

A

neither fnor g is one-one

B

f and g both are necessarily one-one

C

g must be one-one

D

None of the above

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The correct Answer is:
D
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DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 2: Mappings, Mapping of Functions, Kinds of Mapping of Functions)
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  2. The set of parameter 'a' for which the functions f:R to R"defined by"f...

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  3. If A= {1,3,5,7} and B= {1,2,3,4,5,6,7,8}, then the number of one-to-on...

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  4. Which of the following is one-one function ?

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  5. f:X to Y is onto, if and only if 1. range of f=Y 2. range of f neY ...

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  6. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

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  7. Let f: RtoR be function defined by f(x)=sin (2x-3), then f is

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  8. On the set of integers Z, define f : Z to Z as f(n)={{:((n)/(2)",",,...

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  9. If the function f: RvecA given by f(x)=(x^2)/(x^2+1) is surjection, th...

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  10. If f : R -> R be a function such that f(x) = { x|x| -4; x in Q, x|x| -...

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  11. Consider functions f and g such that composite gof is defined and is ...

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  12. If f(x)=|x-2|, where x is a real number, then, which one of the follow...

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  13. Let f : R - {n} rarr R be a function defined by f(x)=(x-m)/(x-n), wher...

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  14. The function f : R -> R is defined by f (x) = (x-1) (x-2) (x-3) is

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  15. Let A = {1, 2, 3) and B= {a,b,c}, and f= {(1, a),(2, b), (P, c)} be a...

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  16. A function f: X to Y is said to be onto, if for every y in Y there ex...

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  17. Let f be a one-one function with domain {x,y,z} and range {1,2,3}. It ...

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  18. The mapping f : N to N given by f(n)=1+n^(2), n in N, where N is the s...

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  19. The function f:R to R given by f(x)=x^(2)+x is

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