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Are f and g both necessarily onto, if gof is onto ?

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

Show that if f:A to B and g: B to C are onto, then gof :A to C is also onto.

Show that if f: A to B and g : B to C are one-one, then gof :A to C is also one-one.

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.

Define an onto function. Give one example. (A) A function f:A to B is said to be an onto function if AA b in EE a in A such that f(a)=b (or) if range of f = codomain of f then f is an onto function. Ex. f: R to R such that f(x) = 2x+3

Let f:(-1,1) to B , be a function defined by f(x) = tan^(-1)((2x)/(1-x^(2))) , then f is both one-one and onto when B is the interval.

Show that the function f:N to N, given by f (1) =f (2) =1 and f (x) =x -1, for every x gt 2, is onto but not one-one.

NCERT TELUGU-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Are f and g both necessarily onto, if gof is onto ?

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  2. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

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  3. Let f:Wto W be defined as f (n)=n -1, if n is odd and f (n) =n +1, if ...

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  4. If f : R to R is defined by f (x) =x ^(2) - 3x + 2, find f (f (x)).

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  5. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

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  6. Show that the function f: R to R given by f (x) = x ^(3) is injective...

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  7. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

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  8. Give examples of two functions f : N to N and g : N to N such g o f is...

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  9. Given a non empty set X, consider P (X) which is the set of all subset...

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  10. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

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  11. Let S = {a,b,c} and T ={1,2,3}. Find F ^(-1) of the following F from S...

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  12. Consider the binary opertions **: R xx R to R and o : R xx R to R defi...

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  13. Given a non-empty set X, let **: P(X) xx P (X) to P (X) be defined as ...

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  14. If A = {0,1,2,3,4,5} Define a binary operation * on A as a*b = {{:(a+b...

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  15. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

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  16. Let A = {1,2,3}. Then number of relations containing (1,2) and (1,3) w...

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  17. Let A = {1,2,3}. Then number of equivalence relations containing (1,2)...

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  18. Let f : R to R be the Signumb Function defined as f (x) = {{:(1",",...

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  19. Number of binary opertions on the set {a,b} are

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