Home
Class 11
MATHS
The relation f is defined by f(x)={x^2,0...

The relation f is defined by `f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10`The relating g is defined by `g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10`Show that f is a function and g is not a function.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    RD SHARMA ENGLISH|Exercise All Questions|100 Videos

  • GEOMETRIC PROGRESSIONS

    RD SHARMA ENGLISH|Exercise All Questions|256 Videos

Similar Questions

Explore conceptually related problems

The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10 The relation g is defined by g(x)={x^2,0lt=xlt=3 3x ,2lt=xlt=10 Show that f is a function and g is not a function.

The relation f is defined by f(x) ={(3x+2", "0le x le2),(x^(3)", "2 le x le 5):}. The relation g is defined by g(x) ={(3x+2", "0le x le1),(x^(3)", "1 le x le 5):} Show that f is a function and g is not a function

Redefine the function f(x)=|x-2|+|2+x|,-3lt=xlt=3

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lt=xlt=2 3-x ,2 2

if f(x)={x^3+x^2,for0lt=xlt=2x+2,for2

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

The function f is defined by f(x)={{:(x+3" if ",xlt1),(x^(2)" if ",xge1):} . Find f(-5),f(1), and f(3) .

Discuss the continuity of the function f, where f is defined by f(x)={{:(3, if0lt=xlt=1),( 4, if1 < x < 3),( 5, if3lt=xlt=10):}

Verify Rolles theorem for the function f(x)=x(x-3)^2,\ 0lt=xlt=3 .

Let f(x)={x/2-1,0lt=xlt=1 1/2,1lt=xlt=2}g(x)=(2x+1)(x-k)+3,0<=x<=oo then g(f(x)) is continuous at x=1 if k equal to:

RD SHARMA ENGLISH-FUNCTIONS-All Questions
  1. If A = {p,q,r, s} and B = {1, 2, 3}, find which of the following is n...

    Text Solution

    |

  2. Let A = {9, 10 , 11 , 12 , 13}and let f : A ->Nbe defined by f(n) = th...

    Text Solution

    |

  3. The relation f is defined by f(x)={x^2,0lt=xlt=3 3x ,3lt=xlt=10The rel...

    Text Solution

    |

  4. If f(x)=x^2, find (f(1. 1)-f(1))/((1. 1-1))

    Text Solution

    |

  5. If f(x)=3x^4-5x^2+9, find f(x-1) .

    Text Solution

    |

  6. If f(x)=1/(2x+1),\ x!=-1/2,\ then show that f(f(x))=(2x+1)/(2x+3) , p...

    Text Solution

    |

  7. If f(x) = x^2 - 3x + 4, then find the values of x satisfying the equat...

    Text Solution

    |

  8. If f(x)=(x-a)^2(x-b)^2, find f(a+b)

    Text Solution

    |

  9. If f(x)=(x+1)/(x-1) , show that f{f(x)}=xdot

    Text Solution

    |

  10. If f(x)= {(x^2,"when" ,xlt0),( x ," when", 0lexlt1),( 1/x ," when", ...

    Text Solution

    |

  11. If f(x)=(2x)/(1+x^2)\ , show that f(tantheta)=sin2theta)

    Text Solution

    |

  12. Find the domain of each of the following real valued function: f(x)=1/...

    Text Solution

    |

  13. Find the domain of each of the following real valued function: f(x)=(x...

    Text Solution

    |

  14. Find the domain of each of the following real valued function: f(x)=(2...

    Text Solution

    |

  15. Find the domain of each of the following real valued function: f(x)=(x...

    Text Solution

    |

  16. Find the domain of the function f(x) defined by f(x)=sqrt(4-x)+1/(sqrt...

    Text Solution

    |

  17. The range of the function f(x) = (x^2-9)/(x-3); x!=3 is

    Text Solution

    |

  18. The domain and range of the real function f defined by f(x)=(4-x)/(x-4...

    Text Solution

    |

  19. The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,...

    Text Solution

    |

  20. Let f ={(x ,(x^2)/(1+x^2)):x in R}be a function from R into R. Determi...

    Text Solution

    |