Home
Class 12
MATHS
Suppose that g(x)=1+sqrt(x) " and " f(g(...

Suppose that `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x.` Then find the function `f(x)`.

Text Solution

Verified by Experts

`g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x " " `(1)
` :. f(1+sqrt(x))=3+2sqrt(x)+x`
Put `1+sqrt(x)=y " or " x=(x-y)^(2).` Then,
`f(y)=3+2(y-1)+(y-1)^(2)=2+y^(2).`
` :. f(x)=2+x^(2)`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.1|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Suppose that g(x)=1+sqrt(x) and f(g(x))=3+2sqrt(x)+xdot Then find the function f(x)dot

Let f(x)=2x-sin x and g(x)=3sqrt(x) . Then

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

Let g(x) be a function defined on [-1,1]dot If the area of the equilateral triangle with two of its vertices at (0,0) a n d (x ,g(x)) is (sqrt(3))/4 , then the function g(x) is (b) g(x)=+-sqrt(1-x^2) (c) g(x)=sqrt(1-x^2) (d) g(x)=-sqrt(1-x^2) (a) g(x)=sqrt(1+x^2)

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find F' (x) if F(x) = sqrt(x^2 -1) .

Find f'(x) if f(x)=sqrt(x^(2)+1)

Find f'(x) if f(x)=sqrt(x^(2)-1)

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. Let f:{2,3,4,5} to {3,4,5,9}and g:{3,4,5,9} to {7,11,15} be functions...

    Text Solution

    |

  2. Let f(x) and g(x) be bijective functions where f:{a,b,c,d} to {1,2,3,4...

    Text Solution

    |

  3. Suppose that g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x. Then find th...

    Text Solution

    |

  4. The function f(x) is defined in [0,1]. Find the domain of f(tanx).

    Text Solution

    |

  5. f( x )={ x+1,x<0 x^2,x>0 and g(x)={ x 3 x<1 2x-1,x>1 find f(g(x)) a...

    Text Solution

    |

  6. If f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2, ...

    Text Solution

    |

  7. Two functions are defined as under : f(x)={(x+1, x le 1), (2x+1, 1 < x...

    Text Solution

    |

  8. Suppose f:A to B " and " B to C. (i) Prove that if f is onto and g i...

    Text Solution

    |

  9. Let f: A to B and g: B to C be two functions. Then; if gof is onto the...

    Text Solution

    |

  10. Which of the following functions has inverse function? a)f: ZrarrZdef...

    Text Solution

    |

  11. Let f:R to [1,oo),f(x)=x^(2)-4x+5. Then find the largest possible int...

    Text Solution

    |

  12. Let A=R-{3},B=R-{1}, and let f: AvecB be defined by f(x)=(x-2)/(x-3) i...

    Text Solution

    |

  13. Let f:R to R be defined by f(x) =e^(x)-e^(-x). Prove that f(x) is inve...

    Text Solution

    |

  14. Find the inverse of f(x)={x ,<1x^2,1lt=xlt=4 8sqrt(x),x >4

    Text Solution

    |

  15. Find the inverse of the function f: [-1,1] to [-1,1],f(x) =x^(2) xx s...

    Text Solution

    |

  16. Find the inverse of the function f:[-(pi)/(2)-"tan"^(1)(3)/(2),(pi)/...

    Text Solution

    |

  17. If f(x)=3x-2a n d(gof)^(-1)(x)=x-2, then find the function g(x)dot

    Text Solution

    |

  18. Let f(x)=x+f(x-1)forAAx in RdotIff(0)=1,fin df(100)dot

    Text Solution

    |

  19. The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a " a...

    Text Solution

    |

  20. Let a function f(x)s a t i sfi e sf(x)+f(2x)+f(2-x)+f(1+x)=AAx in Rdo...

    Text Solution

    |