Home
Class 12
MATHS
Let f(x)=sinx and g(x)=(log)e|x| If the ...

Let `f(x)=sinx and g(x)=(log)_e|x|` If the ranges of the composition functions `fog and gof` are `R_1 and R_2,` respectively then (a) `R_1{u:-1 le u < 1}, R_2={v:-oo v < 0}` (b) `R_1={u:-oo < u < 0}, R_2={v:-oo < v < 0}` (c) `R_1={u:-1 < u < 1},R_2={v:-oo < v le 0}`

Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos
  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f(x) = (1−x)^(1/2) and g(x)=ln(x) then the domain of (gof)(x) is

Find the range of the function f(x) = abs(x - 1) + abs(x - 2) , -1 le x le 3

Let f : R to R be defined as f(x) = (x^2-x+4)/(x^2+x+4) . Then the range of the function f(x) is

Let f,g: R-R be two functions defined as f(x)=|x|+x and g(x)=|x|-x , for all x Then find fog and gof.

Let f(x)=e^({e^(|x|sgnx)})a n dg(x)=e^([e^(|x|sgnx)]),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=ln(f(x))+ln(g(x)) . Then for real x , h(x) is

Draw the graph of the function f : R- {-1, 1} rarr R.f(x)=(x)/(1-|x|) .

Let x in (0,pi/2)dot Then find the domain of the function f(x)=1/sqrt((-(log)_(sinx)tanx))

Let f:R→R: f(x)=x+1 and g:R→R: g(x)=2x−3 . Find (f−g)(x) .

Let f: R to R be defined as f(x) = e^("sgn "x)+ e^(x^(2)) . Then find the range of the function, and also indentify the type of the function : one-one or many-one.

Find the derivatives of the following functions w.r.t. x : 3sec^(-1)x+5e^(log x)-2 tan^(-1)x

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Which of the following functions is periodic?

    Text Solution

    |

  2. The domain of definition of the function y=1/((log)(10)(1-x))+sqrt(x+...

    Text Solution

    |

  3. Let f(x)=sinx and g(x)=(log)e|x| If the ranges of the composition func...

    Text Solution

    |

  4. If a, b be two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2 ...

    Text Solution

    |

  5. Which of the following pairs of functions is/are identical? (a) f(x)=...

    Text Solution

    |

  6. Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer ...

    Text Solution

    |

  7. Which of the following is/are not functions ([.]) and {.} denote the ...

    Text Solution

    |

  8. Find the value of the x/9+y/4, when x=2, y=-3

    Text Solution

    |

  9. Which of the following function is/are periodic? A. f(x)={(1, "x is...

    Text Solution

    |

  10. f(x)=x^2-2a x+a(a+1),f:[a ,oo)vec[a ,oo)dot If one of the solution of ...

    Text Solution

    |

  11. Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R...

    Text Solution

    |

  12. If f: R^+rarrR^+ is a polynomial function satisfying the functional e...

    Text Solution

    |

  13. Suppose that f(x) is a function of the form f(x) =(a x^8+b x^6+c x^4+...

    Text Solution

    |

  14. Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real dis...

    Text Solution

    |

  15. Which of the following functions from A={x in R :-1lt=xlt=1} to its...

    Text Solution

    |

  16. If f: NrarrN,and x2> x1=> f(x2)>f(x1) for x1,x2 in N a n df(f(n))=2nA...

    Text Solution

    |

  17. Find the range of f(x)=(log)3(5-4-x^2)

    Text Solution

    |

  18. The number of iintegral values of a for which f(x)= log(log(1//3)(log(...

    Text Solution

    |

  19. If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

  20. Let f(x)=sin^(23)x-cos^(22)xa n dg(x)=1+1/2tan^(-1)|x| . Then the numb...

    Text Solution

    |