Home
Class 12
MATHS
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`.

Text Solution

Verified by Experts

The correct Answer is:
`ne ` fog
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos

  • VECTOR ALGEBRA

    NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = cos x and g(x) = 3x^2 . Show that gof ne fog.

Find gof and fog , if f (x) = |x| and g(x) = |5x-2| .

Find gof and fog , if f(x) = 8x^(3) and g(x) =x^(1/3)

Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

If f(x) = 8x^3 and g(x) =x^(1/3) then find gof and fog .

If f : R rarr R be given by f(x) = (3-x^(3))^(1/3) then fof (x) is

Consider f : R rarr R given by f(x) = 4x +3. Show that f is invertible. Find inverse of f .

If f : R rarr R and g : R rarr R be two mapping such that f(x) = sin x and g(x) = x^(2) , then find the values of (fog) ((sqrt(pi))/(2)) and (gof)((pi)/(3)) .

If f: R -> R and g: R ->R are two given functions, then prove that 2min {f(x)-g(x),0}=f(x)-g(x)-|g(x)-f(x)|

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

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Find gof and fog, if f : R ->Rand g : R ->Rare given by f(x) = cos xan...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

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

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

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

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |