Home
Class 12
MATHS
Let f(x) and g(x) be bijective functions...

Let f(x) and g(x) be bijective functions where `f:{a,b,c,d} to {1,2,3,4} " and " g :{3,4,5,6} to {w,x,y,z},` respectively. Then, find the number of elements in the range set of `g(f(x)).`

Text Solution

Verified by Experts

The range of `f(x)` for which `g(f(x))` is defined is `{3,4}`.
Hence, the domain of `g{f(x)}` has two elements.
Therefore, the range of `g(f(x))` also has two elements.
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

Let f(x)a n dg(x) be bijective functions where f:{1, b , c , d}vec{1,2,3,4}a n dg:{3,4,5,6}vec{2, x , y , z}, respectively. Then, find the number of elements in the range of g"("f(x)"}"dot

Let A={1, 2, 3, 4} and B=N , Let f:A to B be defined by f(x)=x^(3) then, Find the range of f.

Let A ={ 1,2,3,4,} and B =N. Let f: A to B be defined by f(x) = x^(2) then. find the range of f

Let f(x)=x^(3)+x+1 and let g(x) be its inverse function then equation of the tangent to y=g(x) at x = 3 is

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).

If f and g are continuous functions with f(3) = 5 and lim_(xto3)[2f(x)-g(x)]=4 , find g(3).

Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x),g^(prime)(x) be a , b , respectively, (a

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

Let f(x)=x/(1+x) and let g(x)=(rx)/(1-x) , Let S be the set off all real numbers r such that f(g(x))=g(f(x)) for infinitely many real number x. The number of elements in set S is

Let A={1, 2, 3, 4, 5, 6}, B=W and f:A to is defined by f(x)=x^(2)-1 find the range of f.

CENGAGE-RELATIONS AND FUNCTIONS-Examples
  1. For what integral value of n if 3 pi is the period of the function cos...

    Text Solution

    |

  2. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |