Home
Class 12
MATHS
f(x) =e^x and g(x) = log e^x, then which...

`f(x) =e^x and g(x) = log e^x, then which of the following is TRUE?

A

`f(g(x) )ne g (f(x))`

B

`f(g(x)) = g(f(x))`

C

`f(g(x)) + g (f(x)) = 0`

D

`f (g(x)) - g (f(x)) = 1`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(2cosx-sin2x)/((pi-2x)^(2)) , g(x)=(e^(-cosx)-1)/(8x-4pi) h(x)=f(x) for x lt pi/2 h(x) = g(x) for x gt pi/2 then which of the following holds?

If f(x) = log x and g(x) = e^x then fog(x) is :

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? (a) [f(x)]^(g(x)) is always increasing (b) [f(x)]^(g(x)) is decreasing, when f(x) 1. (d) If f(x)>1,t h e n[f(x)]^(g(x)) is increasing.

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

f(x)={(x-1",",-1 le x le 0),(x^(2)",",0le x le 1):} and g(x)=sinx Consider the functions h_(1)(x)=f(|g(x)|) and h_(2)(x)=|f(g(x))|. Which of the following is not true about h_(1)(x) ?

If f (x) = log x and g (x) = e^X , then (fog) (x) is :

If e^(f(x)) = log x then f'(e) equals

Let f(x) = log x, Evaluate f' (e) .

The domain of the function f(x)=log_(e){log_(|sinx|)(x^(2)-8x+23)-(3)/(log_(2)|sinx|)} contains which of the following interval (s) ?

If f(x) =|log_(e)|x||, then f'(x) equals

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. f(x) =e^x and g(x) = log e^x, then which of the following is TRUE?

    Text Solution

    |

  2. Which one of the following graph represents the function of x? Why?

    Text Solution

    |

  3. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be onto...

    Text Solution

    |

  4. Let A be the set of all 50 students of class XII in a school. Let f: A...

    Text Solution

    |

  5. Prove that the function f : RrarrR given by f (x) = 2x is one-one and...

    Text Solution

    |

  6. Show that the function: f: N rarr N given by f(1) = f (2) = 1 and f (x...

    Text Solution

    |

  7. Show that function f: Rrarr R given by f(x) = x^2 is neither one-one n...

    Text Solution

    |

  8. Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,i...

    Text Solution

    |

  9. If f : R rarr R is defined by f(x) = x + 2, find f(f(x))

    Text Solution

    |

  10. If f : R rarr R be given by: f(x) = (3-x^3)^1//3, then f(f(x)) is:

    Text Solution

    |

  11. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find fog

    Text Solution

    |

  12. If f(x) = (x+1)/(x+2) and g(x) = x^2, then find gof.

    Text Solution

    |

  13. Find gof and fog, if f(x) = |x| and g(x) = |5x -2|

    Text Solution

    |

  14. Let f(x) = (4x+3)/(6x-4), x ne 2/3 .show that fof (x) = x.

    Text Solution

    |

  15. Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = co...

    Text Solution

    |

  16. If the function f : R rarr R given by f(x) = x^2 +2 and g RrarrR be g...

    Text Solution

    |

  17. Let f : { 1, 2, 3} rarr {a, b, c} be one-one and onto function given b...

    Text Solution

    |

  18. Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by ...

    Text Solution

    |

  19. Let Y = {n^2 : n in N} sub N Consider f : N rarr Y as f (n) = n^2 Show...

    Text Solution

    |

  20. Let f: Nrar R be a function defined as : f(x) = 4x^2 + 12 x + 15. Sho...

    Text Solution

    |

  21. Let f : N rarr N be a function deifned by f(x) = 9x^2 + 6x - 5. Show ...

    Text Solution

    |