Home
Class 12
MATHS
If f :[2,oo)rarr(-oo,4], where f(x)=x(4-...

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

Text Solution

Verified by Experts

Given,
`f(x)=x(4-x)`
`y=x(4-x)`
`y=4x-x^2`
`x^2-4x+y=0`
`x=(4+-sqrt(16-4y))/2=f^(-1)x`
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:(-oo,1]rarr(-oo,1] such that f(x)=x(2-x). Then find f^(-1)(x)

If the function f:[2,oo)rarr[-1,oo) is defined by f(x)=x^(2)-4x+3 then f^(-1)(x)=

If f:[1,oo)rarr[1,oo) is defined as f(x)=3^(x(x-2)) then f^(-1)(x) is equal to

If f:[1, oo) rarr [2, oo) is defined by f(x)=x+1/x , find f^(-1)(x)

f:(-oo,oo)rarr(-oo,oo) defined by f(x)=x^(3)

f:(0,oo)rarr(0,oo) defined by f(x)=x^(2) is

Let f:[(1)/(2),oo)rarr[(3)/(4),oo), where f(x)=x^(2)-x+1. Find the inverse of f(x) Hence or otherwise solve the equation,x^(2)-x+1=(1)/(2)+sqrt(x-(3)/(4))

f:(-oo,oo)rarr(-oo,oo) defined by f(x)=|x| is

If f : [1, oo) rarr [2, oo) is given by f(x) = x + (1)/(x) then f^(-1) (x) equals:

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

    |