Home
Class 12
MATHS
A function f : RrarrR is defined as f(x)...

A function `f : RrarrR` is defined as `f(x) = x^(2) +2`, then evaluate each of the following :
(i) `f^(-1)(-6)` (ii) `f^(-1)(18)`

Text Solution

AI Generated Solution

To solve the problem step by step, we need to evaluate the function \( f(x) = x^2 + 2 \) and find the inverse function values for \( f^{-1}(-6) \) and \( f^{-1}(18) \). ### Step 1: Understand the function and its inverse The function is defined as: \[ f(x) = x^2 + 2 \] To find the inverse, we first set \( f(x) = y \): ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1a|18 Videos
  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1b|20 Videos
  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

A function f: R to R is defined as f(x)=x^(2)+1 . Evaluate each of the following: (i) f^(-1)(-2) " "(ii) f^(-1)(17) (iii) f^(-1) (26,50)" "(iv) f^(-1)(0)

If f(x)=2x-5 , then evaluate the following: (i) f(0) (ii) f(7) (iii) f(-3)

A function f: R to R is defined as: f(x) ={{:(1,x in Q),(-1,x notinQ):} Evaluate each of the following: (i) f(2),f(pi)" "(ii) Range of f (iii) f^(-1)(-1)" "(iv) f^(-1)(1)

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

If a function f:R to R is defined as f(x)=x^(2)+1, then find each of the following : (i) {x,f(x)=26} (ii) Pre-image of 17 under f (iii) Pre-image of 2 under f

Let a function f:R^(+) to R is defined as f(x)="log"_(e)x, then find each of the following: (i) Range of f (ii) f(x)=-2 (iii) Is f(xy)=f(x)+f(y) true ?

The function f:R rarr R defined as f(x)=(x^(2)-x+1)/(x^(2)+x+1) is

If a function F: RrarrR is defined as f(x)=int(x^8+4)/(x^4-2x^2+2)dx f (0) =1 , then which of the following is correct ?

A function f is defined by f(x) = x^(2) + 1 . Find f(0), f(5), f(10).

NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
  1. A function f : RrarrR is defined as f(x) = x^(2) +2, then evaluate eac...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Show that the function f: R->{x in R :-1ltxlt1} defined by f(x)=x/(1+...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f: N->Z and g: Z->Z such that gof is...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

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

    Text Solution

    |

  10. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  11. Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...

    Text Solution

    |

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

    Text Solution

    |

  13. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

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

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |