Home
Class 11
MATHS
If f: [0,3] to [0,3] is defined by: f...

If `f: [0,3] to [0,3]` is defined by:
`f(x) = {{:(1+x,0 le x le 2),(3-x, 2 lt x le 3):}` , then show that `f[0,3] sube [0,3]` and find fof.

Text Solution

Verified by Experts

The correct Answer is:
`therefore (fof)(x) = {{:(2+x, 0 le x le 1),(2-x, 1 lt x le 2),(4-x, 2 lt x le 3):}`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE -1.1 (VERY SHORT ANSWER QUESTIONS)|21 Videos

  • FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE -1.2 (VERY SHORT ANSWER TYPE QUESTIONS)|2 Videos

  • ERRORS AND APPROXIMATIONS

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTION|15 Videos

  • HEIGHTS AND DISTANCES

    AAKASH SERIES|Exercise PRACTICE SHEET Exercise-I (Level-II) (Straight Objective Type Questions)|13 Videos

Similar Questions

Explore conceptually related problems

If f: R to R defined by f(x) ={{:(2x+5, if, x gt 0),(3x-2, if, x le 0):} then f is

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f(x) is increasing in [-1, 2]

If f is defined by f (x) = {:{ (x , " for " 0 le x lt 1) , ( 2 -x , " for " x le 1 ) :} then at x =1

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f(x) has maximum value at x = 2.

If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x le 3):} , show that f'(x) does not exist at x = 2

Show that f(x)={{:(x^(2),if, 0 le x le 1),(x ,if, 1 le x le 2):} is continuous on [0,2]

If f: A to A is defined by f(x) =x^(3) , where A ={x//-1 le x le 1} , then f is

Suppose f:[-2, 2] rarr RR is defined by f(x)={{:(-1" for "-2 le x le 0),(x-1" for "0le xle 2):} , then {x in [-2, 2]: x le 0 and f(|x|)=x}=

AAKASH SERIES-FUNCTIONS -PRACTICE EXERCISE
  1. If f: [0,3] to [0,3] is defined by: f(x) = {{:(1+x,0 le x le 2),(3-...

    Text Solution

    |

  2. If f(x)=(3x-7)/(5x-3) then (fof)(x)=

    Text Solution

    |

  3. If f:RR rarrRR and g:RR rarrRR are defined by f(x)=2x+3 and g(x)=x^(2)...

    Text Solution

    |

  4. f: R to R is defined by f(x) =x^(2)-5x. Then the inverse image set of ...

    Text Solution

    |

  5. If f: R to [0, infty) defined by f(x) = 10^(x) then f^(-1)(x)=

    Text Solution

    |

  6. The range of 10^(-x) is:

    Text Solution

    |

  7. The range of |x-2|+|x-5| is:

    Text Solution

    |

  8. If A, B are two sets such that n(A) = 15, n(B) = 20, then the number o...

    Text Solution

    |

  9. The number of surjections that can be defined from {1, 2, 3, 4, 5} ont...

    Text Solution

    |

  10. The number of constant functions that can be defined from {1, 2, ……….,...

    Text Solution

    |

  11. If f, g, h are functions from R to R such that f(x) = x^(2)+1, g(x) =s...

    Text Solution

    |

  12. If f(x)=sin(logx), then f(xy)+f(x//y)-2f(x)cos (logy)=

    Text Solution

    |

  13. If f(x)=(1)/(2)[3^(x)+3^(-x)], g(x)=(1)/(2)[3^(x)-3^(-x)] then f(x)g(y...

    Text Solution

    |

  14. If f(x) =cos[pi^(2)]x + cos[-pi^(2)]x where [x] is symmetrical about t...

    Text Solution

    |

  15. The graph of the function y = f(x) is symmetrical about the line x = 3...

    Text Solution

    |

  16. Let f(x) = ax^(3) + bx +c. Then when f is odd,

    Text Solution

    |

  17. a) The number of elements in the range of a constant function. (b) I...

    Text Solution

    |

  18. The value of parameter alpha, for which the function f(x) =1+alphax, a...

    Text Solution

    |

  19. Let f:[4, infty) to [1, infty) be a function defined by f(x) = 5^(x(x-...

    Text Solution

    |

  20. If f: R to R and g: R to R are defined by f(x) =3x-4, g(x)=2+3x and 2(...

    Text Solution

    |

  21. The domain of the definition of the function f(x) = sqrt(4^(x) + 8^(...

    Text Solution

    |