Home
Class 12
MATHS
Show that functions f and g defined by f...

Show that functions f and g defined by f(x)=2 log x and g(x)`=log x^2` are not equal even though log `x^2 =2 log x.

Text Solution

Verified by Experts

`f(x)=2 "log"x`
`g(x)="log" x^2`
`"Dom" f(x) = (0,oo)`
`"Dom" g(x) =R-{0} `
`"As Dom" f(x) != Dom g(x) "we have" f(x) !=g(x), "though log" x^2 =2"log"x`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    MBD PUBLICATION|Exercise QUESTION BANK|171 Videos

  • RELATIONS AND FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|106 Videos

Similar Questions

Explore conceptually related problems

If f:RrarrR and g:RrarrR is defined by f(x)=sinx and g(x)=5x^2 , then (gof)(x).

Determine f(0) so that the function f(x) defined by f(x)=((4^(x)-1)^(3))/("sin "(x)/(4)"log"(1+(x^(2))/(3))) becomes continuous at x=0 .

If f(x)=log_x^(2)(logx) , then f(e)

Solve the following differential equations. x log x dy/dx +y=2 log x

Let f: R rarr R be defined by f(x) = 2x - 3 and g: R rarr R be defined by g(x) = (x+3)/(2) , show that fogʻ= I_(R)

MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Show that f(x) = loga x "on" (0,oo ),(a gt 0 "and" a != 1) functions a...

    Text Solution

    |

  2. Show that f(x)=a^x "on" R.(a gt 0 "and" a != 1) functions are injectiv...

    Text Solution

    |

  3. Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 a...

    Text Solution

    |

  4. Give an example of a function which is Surjective but not injective.

    Text Solution

    |

  5. Give an example of a function which is injective but not surjective.

    Text Solution

    |

  6. Give an example of a function which is neither injective nor surjectiv...

    Text Solution

    |

  7. Give an example of a function which is bijective

    Text Solution

    |

  8. Prove that {1,2,3,4,5,6,……} set are equivalent.

    Text Solution

    |

  9. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

    Text Solution

    |

  10. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

    Text Solution

    |

  11. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

    Text Solution

    |

  12. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

    Text Solution

    |

  13. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

    Text Solution

    |

  14. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

    Text Solution

    |

  15. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  16. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

    Text Solution

    |

  17. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

    Text Solution

    |

  18. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  19. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |

  20. Find the composition fog and gof and test whether fog = gof when f and...

    Text Solution

    |