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Let f : {2, 3, 4, 5}-> {3, 4, 5, 9}and g...

Let `f : {2, 3, 4, 5}-> {3, 4, 5, 9}`and `g : {3, 4, 5, 9} ->{7, 11 , 15}`be functions defined as `f (2) = 3`, `f (3) = 4`, `f (4) = f (5) = 5`and `g (3) = g (4) = 7 and g (5) `

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To solve the problem, we need to find the composite function \( g \circ f \) which means we will evaluate \( g(f(x)) \) for each \( x \) in the domain of \( f \). ### Step-by-Step Solution: 1. **Identify the Functions**: - The function \( f : \{2, 3, 4, 5\} \to \{3, 4, 5, 9\} \) is defined as: - \( f(2) = 3 \) - \( f(3) = 4 \) ...
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Let f:{2,3,4,5} to {3,4,5,9}and g:{3,4,5,9} to {7,11,15} be functions defined as f(2)=3,f(3)=4, f(4)=f(5)=5, g(3)=g(4)=7, " and " g(5)=g(9)=11. " Find " gof.

Let f:{2,3,4,5}rarr{3,4,5,9}a n d g:{3,4,5,9}rarr{7,11,15} be functions defined at f(2)=3,f(3)=4,f(4)=f(5)=5,g(3)=g(4)=7, a ndg(5)=g(9)=11. Find g(f(x))

If f'(4)=5, f(4)=3, g'(6)=7 and R(x)=g[3+f(x)] then R'(4)=

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

Let f:" "{1," "3," "4}-> {1," "2," "5} and g:" "{1," "2," "5} ->{1," "3} be given by f" "=" "{(1," "2)," "(3," "5)," "(4," "1)} and g" "=" "{(1," "3)," "(2," "3)," "(5," "1)} . Write down gof .

If f(x) = -2x +7 and g(x)=x^(2)-5x +6 find f(3), f(-4), g(2) and g(-1) .

Let A = {1,2,3,4} and f : A to A satisfy f (1) =2, f(2)=3, f(3)=4, f (4)=1. Suppose g:A to A satisfies g (1) =3 and fog = gof , then g =

Let A={1,2,3},B={5,6,7} and f:A to B be a function defined as f={(1,6),(2,5),(3,7)} Then f is :

NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Show that if f : A ->Band g : B ->Care onto, then gof : A ->Cis also ...

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  2. Show that if f : A ->Band g : B ->Care one-one, then gof : A ->Cis al...

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  3. Let f : {2, 3, 4, 5}-> {3, 4, 5, 9}and g : {3, 4, 5, 9} ->{7, 11 , 15}...

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  4. Show that a one-one function f : {1, 2, 3}-> {1, 2, 3}must be onto.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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