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Find gof and fog, if f : R ->Rand g : R ...

Find gof and fog, if `f : R ->R`and `g : R ->R`are given by `f(x) = cos x`and `g(x)=3x^2`. Show that `gof!=fog`.

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To solve the problem, we need to find the compositions of the functions \( f \) and \( g \), specifically \( g \circ f \) and \( f \circ g \), and show that they are not equal. ### Step 1: Define the Functions We have: - \( f(x) = \cos x \) - \( g(x) = 3x^2 \) ### Step 2: Find \( f \circ g \) ...
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Show that a one-one function f : {1, 2, 3}-> {1, 2, 3}must be onto.

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  2. Show that if f: R-{7/5}->R-{3/5}is defined by f(x)=(3x+4)/(5x-7)and g...

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  3. Find gof and fog, if f : R ->Rand g : R ->Rare given by f(x) = cos xan...

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  4. Show that the function f : R ->R, defined as f(x)=x^2, is neither one-...

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  5. Show that the function f: N->N given by f(1)=f(2)=1 and f(x)=x-1 for e...

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  6. Show that an onto function f : {1, 2, 3} ->{1, 2, 3}is always one-one...

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  7. Show that f: N to N given by f(x)={(x+1,"if x is odd"),(x-1,"if x ...

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  8. Show that the function f: N->N , given by f(x)=2x , is one-one but not...

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  9. Prove that the function f : R ->R, given by f (x) = 2x, is one-one and...

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  10. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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  11. Let A be the set of all 50 students of class X I I in a central scho...

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  12. Show that the relation R in the set {1, 2, 3}given by R = {(1, 1), (2...

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  13. Show that the relation R on the set Z of integers, given by R={(a ,\ b...

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  14. Let "T" be the set of all triangles in a plane with "R" as relation ...

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  15. Let L be the set of all lines in a plane and R be the relation in L de...

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  16. Let A be the set of all students of a boys school. Show that the rela...

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  17. Show that – a is the inverse of a for the addition operation '+' on R ...

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  18. Show that zero is the identity for addition on R and 1 is the identit...

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  19. Show that the vv: R ->R given by (a , b)->m a x {a , b}and the ^^: R -...

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  20. Let P be the set of all subsets of a given set X. Show that uu: P xx ...

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