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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 \( g \) and \( f \) defined as follows: - \( f(x) = \cos x \) - \( g(x) = 3x^2 \) We will find \( g \circ f \) (denoted as \( g(f(x)) \)) and \( f \circ g \) (denoted as \( f(g(x)) \)) and then show that these two compositions are not equal. ### Step 1: Find \( g \circ f \) ...
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NCERT ENGLISH-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)an...

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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. If A={1,\ 2,\ 3} , show that an onto function f: A->A must be one-o...

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  7. Show that f\ : NvecN ,\ given by f(x)={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 f: R->R , given by f(x)=2x , is one-one and onto.

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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 a relation in T g...

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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 a...

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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 F: R ->R given by (a , b)->m a x {a , b}and the G: R ->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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