Home
Class 12
MATHS
Let f(x)=x^3 be a function with domai...

Let `f(x)=x^3` be a function with domain {0, 1, 2, 3}. Then domain of `f^(-1)` is (a) {3, 2, 1, 0} (b) {0, -1, -2, -3} (c) {0, 1, 8, 27} (d) {0, -1, -8, -27}

Text Solution

AI Generated Solution

To find the domain of the inverse function \( f^{-1} \) for the function \( f(x) = x^3 \) with the specified domain \( \{0, 1, 2, 3\} \), we will follow these steps: ### Step 1: Identify the function and its domain We have the function: \[ f(x) = x^3 \] with the domain: ...
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos
  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^(2)-1)

Let f(x) be a function whose domain is [-5,7] and g(x)=|2x+5|, then the domain of fog(x) is (A) [-5,1](B)[-4,0] (C) [-6,1]( D) none of these

If f(x) is defined on [0,1], then the domain of f(3x^(2)) , is

the domain of the function f(x) = sin^(-1) (2x) is (a) [0,1] (b) [-1,1] (c) [ (-1/2), (1/2) ] (d) [-2,2]

If f(x)=x^(1/3)(x-2)^(2/3) for all x, then the domain of f' is x in R-{0} b.{x|x:)0} c.x in R-{0,2} d.x in R

The function f(x) is defined on the interval [0,1]. What are the domains of definition of functions. (a) f(sin x), (b) f(2x+3)?

If domain of f(x) is [1,3], then the domain of f(log_(2)(x^(2)+3x-2)) is [-5,-4]uu[1,2]b[-13,-2]uu[(3)/(5),5] c.[4,1]uu[2,7] d.{-3,2}

The domain of f(x)=log|log x|is(0,oo)(b)(1,oo)(c)(0,1)uu(1,oo)(d)(-oo,1)

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then f(x)=sin^2x ,g(x)...

    Text Solution

    |

  2. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  3. If the function f:(1,)vec(1,oo) is defined by f(x)=2^(x(x-1)),t h e nf...

    Text Solution

    |

  4. Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=x for all x in R (b) ...

    Text Solution

    |

  5. If the function f: R->R be such that f(x) = x-[x], where [x] denotes t...

    Text Solution

    |

  6. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals....

    Text Solution

    |

  7. Let g(x)=1+x-[x]a n df(x)={-1, x<0 0, x=0f, x >0 . Then for all x ,f(g...

    Text Solution

    |

  8. Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x)...

    Text Solution

    |

  9. If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

    Text Solution

    |

  10. If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) e...

    Text Solution

    |

  11. If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible ...

    Text Solution

    |

  12. If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x)...

    Text Solution

    |

  13. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3...

    Text Solution

    |

  14. Let f(x)=x^3 be a function with domain {0, 1, 2, 3}. Then domain of...

    Text Solution

    |

  15. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3...

    Text Solution

    |

  16. Let f: R->R be given by f(x)=tanx . Then, f^(-1)(1) is pi/4 (b) {npi+p...

    Text Solution

    |

  17. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

    Text Solution

    |

  18. If the set A contains 5 elements and the set B contains 6 elements, th...

    Text Solution

    |

  19. If the set A contains 7 elements and the set B contains 10 elements, ...

    Text Solution

    |

  20. Let f: R-{3/5}->R be defined by f(x)=(3x+2)/(5x-3) . Then

    Text Solution

    |