Home
Class 12
MATHS
Consider f:N to N, g : N to N and h: N t...

Consider `f:N to N, g : N to N and h: N to R` defined as `f (x) =2x,g (h) = 3y + 4 and h (z= sin z, AA x, y and z `in N. Show that h(gof) = (hog) of.

Text Solution

Verified by Experts

The correct Answer is:
(hog) o f
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.1|16 Videos

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.2|12 Videos

  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT BANGLISH|Exercise Miscellaneous Exercise on chapter 10|19 Videos

Similar Questions

Explore conceptually related problems

Let f:N to Y be a function defined as f (x) =4x +3, where, Y = {y in N : y = 4x +3 for some x in N }. Show that f is invertible. Find the inverse.

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Consider the identity function I_(N):N to N defined as I _(N) (x)=x AA x in N. Show that although I _(N) is onto but I _(N) + I _(N) : N to N defined as (I _(N) + I _(N)) (x) = I _(N) (x) + I _(N) (x) x +x = 2x is not onto.

Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an into function.

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If n(x) = 4, n (Y) = 3 and n(X xx Y xx Z) = 24 , then the value of n(Z) is

If a^(x) = b^(y) = c^(z) and a, b, c, are in G.P., prove that x, y, z are in H.P.

If a, b a n d c are in A.P., a x ,b y ,a n dc z in G.P. and x,y,z in H.P. then prove that x/z+z/x=a/c+c/a .

Let A={x,y,z,t} and the function f:A rarr A, g: A rarr A be defined by, f(x)=z, f(y)=t,f(z)=y, f(t)=x and g(x)=y,g(y)=t,g(z)=x,g(t)=z Find (gof) (t),(fog) (x),(f o g ) (y) and (g o f) (z) .

Let F : R to R be such that f is injective and f(x) f(y) =f(x+y) for all x,y in RR If f(x) , f(y) , f(z) are in G.P ., then x,y,z are in -

NCERT BANGLISH-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1
  1. Consider f:N to N, g : N to N and h: N to R defined as f (x) =2x,g (h)...

    Text Solution

    |

  2. Let f : R to R be defined as f (x) =10 x +7. Find the function g : R t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f...

    Text Solution

    |

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

    Text Solution

    |

  7. Give examples of two functions f:N to Z and g: Z to Z such that g o f ...

    Text Solution

    |

  8. Give examples of two functions f : N to N and g : N to N such g o f is...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Find the number of all onto functins from the set {1,2,3..,n} to itsel...

    Text Solution

    |

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

    Text Solution

    |

  13. Show that +:R×R→R and o:R×R→R defined as a∗b=∣a−b∣ and aob=a for all a...

    Text Solution

    |

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

    Text Solution

    |

  15. Define a binary opertion ** on the set {0,1,2,3,4,5} as a**b ={{:(a+...

    Text Solution

    |

  16. Let A = {-1,0,1,2},B= {-4,-2,0,2}and f , g , A to B be functions defin...

    Text Solution

    |

  17. Let A={1,2,3}. Then the number of relations containing (1,2) and (1,3)...

    Text Solution

    |

  18. Let A = {1,2,3},B={5,6.7} then find AcapB

    Text Solution

    |

  19. Let f: R → R be the Signum Function defined as f(x)={ 1, x>0 0, x=0−1,...

    Text Solution

    |

  20. Number of binary opertions on the set {a,b} are

    Text Solution

    |