Home
Class 11
MATHS
Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt...

Let `f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):}`
Determine the form of g(x) = f[f(x)] and hence find the points of discontinuity of g, if any.

Text Solution

Verified by Experts

{1, 2}
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the continuity of f, f' on [0, 2].

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

The function f(x) is defined in 0 le x le1, find the domain of definition of f(x^2)

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Let f(x) = {{:(x^(2) + 3x",", -1 le x lt 0),(-sin x",", 0 le x lt pi//2),(-1 - cos x",", (pi)/(2) le x le pi):} . Draw the graph of the function and find the following (a) Range of the function (b) Point of inflection (c) Point of local minima

If f (x) ={{:(x",", "when " 0 lt x lt 1),(2-x",", "when" 1 lt x le 2):} then f'(1) is equal to-

Given, A={x:0 lt x le2} and B={x:1 lt x lt3}, find A-B

Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3) . Then find g'(x) in terms of g(x).

Let f(x) = 1 + 4x - x^(2), AA x in R g(x) = max {f(t), x le t le (x + 1), 0 le x lt 3} = min {(x + 3), 3 le x le 5} Verify conntinuity of g(x), for all x in [0, 5]

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

PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. A real valued function satisfies the relation f(x+y)=f(x)+f(y)+(e^x-1)...

    Text Solution

    |

  2. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

    Text Solution

    |

  3. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Determine the for...

    Text Solution

    |

  4. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the conti...

    Text Solution

    |

  5. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

    Text Solution

    |

  6. Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x<1...

    Text Solution

    |

  7. Let m and n be two positive integers greater than 1. if lim(alphararr0...

    Text Solution

    |

  8. The correct statement(s) is (are)

    Text Solution

    |

  9. Let f(x) be a polynomial of degree four having extreme values at x=1 a...

    Text Solution

    |

  10. lim(xrarr0)((1-cos2x)(3+cosx))/(xtan4x) is equal to:

    Text Solution

    |

  11. If the function . g(x)={(ksqrt(x+1),0lexle3),(mx+2,3ltxle5):}is differ...

    Text Solution

    |

  12. Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x i...

    Text Solution

    |

  13. If lim(xrarr0)(axe^x-blog(1+x))/x^2=3 ,then the values of a ,b are res...

    Text Solution

    |

  14. Let [x]denote the greatest integer less than or equal to x . Then the ...

    Text Solution

    |

  15. Let f:RrarrR be differentiable at x=0 . If f(0)=0 and f'(0)=2,then the...

    Text Solution

    |

  16. Let f:RrarrR be such that f(2x-1)=f(x) for all x in R . If f is contin...

    Text Solution

    |

  17. Let fbe any continuously differentiable function on [a,b] and twice di...

    Text Solution

    |

  18. Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be ...

    Text Solution

    |

  19. Letf:RrarrR and g:RrarrR be respectively given by f(x)=|x|+1 and g(x)=...

    Text Solution

    |

  20. The largest value of the non-negative integer a for which lim(xrarr1){...

    Text Solution

    |