Home
Class 12
MATHS
If f(x)=logex and g(x)=e^x, prove that f...

If `f(x)=log_ex and g(x)=e^x`, prove that `f{g(x)}=g{f(x)}`.

Promotional Banner

Topper's Solved these Questions

  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Short Answer Type Question|60 Videos
  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Long Answer Type Questions|72 Videos
  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Multiple choice question|28 Videos
  • REAL NUMBERS

    CHHAYA PUBLICATION|Exercise Exercise (Long Answer Type Questions)|10 Videos
  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|3 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log_(3)xandg(x)=x^(2) , then prove that f(g(3)) = 2.

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

If f(x) = ax + b and g(x) = cx + d, then f(g(x))=g(f(x)) implies

If f(x)= sin^(2)x and g(f(x))=|sin x|, then g(x)=

Let the functions f and g on the set of real numbers RR be defined by, f(x)= cos x and g(x) =x^(3) . Prove that, (f o g) ne (g o f).

Let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=x+1 and g(x)=x-1 Prove that , (g o f)=(f o g)=I_(RR)

If f(x)=e^x and g(x) =log_(e)x, then find (f+g)(1) and fg(1).

If f(x)=log_ex is defined in [1,e], then

If the inverse function of y=f(x) is x=g(y) and f'(x)=(1)/(1+x^(2)) , then prove that g'(x)=1+[g(x)]^(2) .

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

CHHAYA PUBLICATION-RELATION AND MAPPING -Very short answer type questions
  1. If f(x)=5^x , then prove : f(x+y)=f(x).f(y)

    Text Solution

    |

  2. If f(x)=5^x , then prove : (f(x+1))/(f(x-1))=25

    Text Solution

    |

  3. If f(x)=5^x , then prove : f(log5x)=x

    Text Solution

    |

  4. If f(x)=a.(x-b)/(a-b)+b.(x-a)/(b-a), show that, " "f(a)+f(b)=f(a...

    Text Solution

    |

  5. If phi(x)=logex, then show: phi(e^x)=x

    Text Solution

    |

  6. If phi(x)=logex, then show: phi(x^m)= mphi(x)

    Text Solution

    |

  7. If phi(x)=logex, then show: phi(xy)=phi(x)+phi(y)

    Text Solution

    |

  8. If phi(x)=logex, then show: phi(x/y)=phi(x)-phi(y)

    Text Solution

    |

  9. If f(x)=e^(px+q) [p and q are constants], show that, f(a).f(b).f(c)=...

    Text Solution

    |

  10. If f(x)=|x|-2x , find f(-1),f(1) and f(-h).

    Text Solution

    |

  11. If g(x)=(x-a)/(x)+(x)/(x-b) , prove that, g((a+b)/(2))=(4ab)/(a^2-b^2)

    Text Solution

    |

  12. If f(x)=(1)/(x^2) , show that f(x+h)-f(x-h)=-(4xh)/((x^2-h^2)^2).

    Text Solution

    |

  13. If g(theta)=(1-tantheta)/(1+tan theta) , find the value of g(pi/4-thet...

    Text Solution

    |

  14. If f(x)=loge.(1+x)/(1-x) , show that f((2x)/(1+x^2))=2f(x).

    Text Solution

    |

  15. If f(x)=logex and g(x)=e^x, prove that f{g(x)}=g{f(x)}.

    Text Solution

    |

  16. If f(x)=10x^2 - 13x+13 solve the equation f(x) = 16.

    Text Solution

    |

  17. If f(x)=4[x]-3|x|, find f(3.5) and f(-3.5).

    Text Solution

    |

  18. If RR is the set of real numbers and f(x)=|x|,g(x)=x, find the product...

    Text Solution

    |

  19. Find the value of [-3]+[-3.6]-|2.6|+|-3|.

    Text Solution

    |

  20. If f (x) =(x-1)/(x+1), then the value of f (2x) in terms of f(x) is-

    Text Solution

    |