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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.

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For x != 0, 1 , define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let G be a function such that GOf_(3)=f_(6) . Then G is equal to

For x != 0, 1 , define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let F be a function such that f_(1)OF=f_(4) . Then F is equal to

For x != 0, 1 , define f_(1)(x)=x, f_(2)(x)=1/x, f_(3)(x)=1-x, f(5) (x)=(x-1)//x, f_(6)(x)=x//(x-1) This family of functions is closed under composition that is , the composition of any two of these functions is again one of these. Let H be a function such that f_(4)OH=f_(5) . Then H is equal to

Determine whether the function f:R to (0,oo) defined by f(x) = 2^(x) is one one (or) onto (or) bijection.

Let f(x) = sinx and g(x) = log|x| .If the ranges of composite functions fog and gof are R_1 and R_2 repsectively, then

NCERT TELUGU-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Consider functions f and g such that composite gof is defined and is o...

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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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