Home
Class 12
MATHS
Let f :[1/2,oo)rarr[3/4,oo), where f(x)=...

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.`

Text Solution

Verified by Experts

The correct Answer is:
x=1
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-I|47 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level-II|20 Videos

  • FUNCTION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-I|24 Videos

  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • HEIGHTS & DISTANCE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II|20 Videos

Similar Questions

Explore conceptually related problems

Find the inverse of f(x)=2^(log_(10)x)+8 and hence solve the equation f(x)=f^(-1)(x)

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

A function f: [3/2, oo) to [ 7/4, oo) defined as, f(x) = x^2 - 3x +4. Then compute f^(-1)(x) and find the solution of the equation, f(x) = f^(-1) (x) .

If f:[1, oo) rarr [2, oo) is defined by f(x)=x+1/x , 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 : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)) , then f is

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

Let f : [-1, -1/2] rarr [-1, 1] is defined by f(x)=4x^(3)-3x , then f^(-1) (x) is

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

let f:[(7)/(4),oo)rarr[(3)/(2),oo) be defined by f(x)=(3)/(2)+sqrt(x-(7)/(4)) and g(x) be the inverse of f(x) then the value of (f^(-1)og^(-1))(17) is equal to

FIITJEE-FUNCTION-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level-II
  1. Let f : {x,y, z} to {a, b, c} be a one-one function. If it is known th...

    Text Solution

    |

  2. Let S be the set of non-negative integers. A function f: S to S is suc...

    Text Solution

    |

  3. Find the range of f(x), where f(x)=cos(sin(In(x^2+e)/(x^2+1)))+sin(cos...

    Text Solution

    |

  4. Consider two functions, f(x) and g(x) defined as under: f(x)={1+x^3,x ...

    Text Solution

    |

  5. If the functions f and g defined from the set of real number R to R su...

    Text Solution

    |

  6. If the functions f, g and h are defined from the set of real numbers R...

    Text Solution

    |

  7. Let f(x)=2cos^2x+sqrt(3)*sin2x+1. Then, its domain and range, so that ...

    Text Solution

    |

  8. Let f: XtoY be a function defined by f(x) =asin(x+(pi)/4) + bcosx + c....

    Text Solution

    |

  9. Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

    Text Solution

    |

  10. Solve the following equations x^(2)-3-{x}=0 where [x] denotes the ...

    Text Solution

    |

  11. Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y)...

    Text Solution

    |

  12. If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and ...

    Text Solution

    |

  13. Let f be a function from be set of positive integers to the set of rea...

    Text Solution

    |

  14. Let f be a function from be set of positive integers to the set of rea...

    Text Solution

    |

  15. If the range of the function f(x)=(x-1)/(p-x^2+1) does not contain any...

    Text Solution

    |

  16. Let f :[1/2,oo)rarr[3/4,oo), where f(x)=x^2-x+1. Find the inverse of f...

    Text Solution

    |

  17. Let f(x) be a function such that : f(x - 1) + f(x + 1) = sqrt3 f(x), f...

    Text Solution

    |