Home
Class 12
MATHS
If f(x)=ax+b and the equation f(x)=f^(-1...

If f(x)=ax+b and the equation `f(x)=f^(-1)(x)` be satisfied by every real value of x, then

A

a=2, b=-1

B

`a=-1,b in R`

C

`a=1, b in R`

D

a=1, b=-1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

If f (x) =x^3-1/x^3 , find the value of f (x) +f (1/x) .

If f (x) satisfies the relation : 2 f(x) +f (1 -x) = x^2 for all real x, then f (x) is :

If f(x)=sin(3x)/sin x,x!=npi , then the range of values of f(x) for real values of x is

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x , then prove that f(x) is periodic and find its period.

If f(X) = (ax-b)/(bx-a) , show that f(f(x)) = x

Let f(x) be a polynominal with real coefficients such that xf(x)=f'(x) times f''(x). If f(x)=0 is satisfied x=1,2,3 only, then the value of f'(1)f'(2)f'(3) is

Let y=f(x) be a differentiable function such that f(−1)=2,f(2)=−1 and f(5)=3 If the equation f (x)=2f(x) has real root. Then find f(x)

Let f:R->R be a function satisfying f((x y)/2)=(f(x)*f(y))/2,AAx , y in R and f(1)=f'(1)=!=0. Then, f(x)+f(1-x) is (for all non-zero real values of x ) a.) constant b.) can't be discussed c.) x d.) 1/x

Suppose f(x)=e^(ax)+e^(bx), where aneb and f''(x)-2f'(x)-15f(x)=0 for all x, then the value of |a+b| is equal to......

Suppose f(x)= {(a+bx,x 1):} and if lim_(x rarr 1)f(x)=f(1) what are possible values of a and b ?

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x)=ax+b and the equation f(x)=f^(-1)(x) be satisfied by every rea...

    Text Solution

    |

  2. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  6. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  13. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  19. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  21. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |