Home
Class 12
MATHS
If f(x) is an invertible function and g(...

If `f(x)` is an invertible function and `g(x)=2f(x)+5,` then the value of `g^(-1)(x)i s`

A

`2f^(-1)(x)-5`

B

`(1)/(2f^(-1)(x)+5)`

C

`(1)/(2) f^(-1)(x)+5`

D

`f^(-1)((x-5)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
Replacing x by `g^(-1)(x),` we get `x=2f(g^(-1)(x))+5`
` :. f(g^(-1)(x))=(x-5)/(2)`
` :. g^(-1)(x)=f^(-1)((x-5)/(2))`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x^(3)+3x+4 and g is the inverse function of f(x), then the value of (d)/(dx)((g(x))/(g(g(x)))) at x = 4 equals

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5x-2, x!=2. Then value of f^(-1)(13) is________

Let f be a real-valued invertible function such that f((2x-3)/(x-2))=5x-2, x!=2. Then value of f^(-1)(13) is________

If g is the inverse of a function f and f(x)=1/(1+x^5) , Then g'(x) i equal to :

Let R be the set of real numbers and the mappings f:R toR" and "g:RtoR be defined by f(x)=5-x^2" and " g(x)=3x-5 , then the value of (f@g)(-1) is

If g is the inverse of a function f and f'(x)=(1)/(1+x^(5)) , then g'(x) is equal to-

If f(x) = [x] and g(x)=|x| the value of f(g(8/5))-g(f(-8/5)) is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2) . Then the value of the integral int_(0)^(1) f(x)g(x) dx is equal to -

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible ...

    Text Solution

    |

  2. Let f: Xrarryf(x)=sinx+cosx+2sqrt(2) be invertible. Then which XrarrY ...

    Text Solution

    |

  3. If f(x) is an invertible function and g(x)=2f(x)+5, then the value of ...

    Text Solution

    |

  4. Discuss the differentiability of f(x) =[x]+ sqrt({x})), where [.] an...

    Text Solution

    |

  5. If f is a function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) fo...

    Text Solution

    |

  6. A function f(x) satisfies the functional equation x^2f(x)+f(1-x)=2x-x^...

    Text Solution

    |

  7. If f(x) is a polynomial satisfying f(x)f(1/x)=f(x)+f(1/x)a n df(3)=28 ...

    Text Solution

    |

  8. If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (...

    Text Solution

    |

  9. Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(...

    Text Solution

    |

  10. If f(x+y)=f(x)+f(y)-x y-1AAx , y in R and f(1)=1, then the number of ...

    Text Solution

    |

  11. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x-1)...

    Text Solution

    |

  12. Let f: RvecR be a continuous and differentiable function such that (f(...

    Text Solution

    |

  13. Let g(x)=f(x)-1. If f(x)+f(1-x)=2AAx in R , then g(x) is symmetrical ...

    Text Solution

    |

  14. If f(x+1)+f(x-1)=2f(x) and f(0)=0, then find f(n),n in N , is

    Text Solution

    |

  15. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

    Text Solution

    |

  16. If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,then f(2) is equal to

    Text Solution

    |

  17. If f(3x+2)+f(3x+29)=0x in R , then the period of f(x) is (a) 7 (b) 8 ...

    Text Solution

    |

  18. If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, the...

    Text Solution

    |

  19. Find f(x) when it is given by f(x)=max{x^(3),x^(2),(1)/(64)},AA x in...

    Text Solution

    |

  20. The equation ||x-2|+a|=4 can have four distinct real solutions for x i...

    Text Solution

    |