Home
Class 12
MATHS
Let f(x)=x^2a n dg(x)=sinxfora l lx in ...

Let `f(x)=x^2a n dg(x)=sinxfora l lx in Rdot` Then the set of all `x` satisfying `(fogogof)(x)=(gogof)(x),w h e r e(fog)(x)=f(g(x)),` is (a) `+-sqrt(npi),n in {0,1,2, dot}` (b)`+-sqrt(npi),n in {1,2, dot}` (c) `pi/2+2npi,n in { ,-2,-1,0,1,2}` (d) `2npi,n in { ,-2,-1,0,1,2, }`

A

`pm sqrt(npi), n in {0,1,2,...}`

B

`pm sqrt(npi), n in {1,2,...}`

C

`pi//2+2npi, n in {...,-2,-1,0,1,2,...}`

D

`2npi, n in {...,-2,-1,0,1,2,...}`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 8:Questions Asked in Previous 10 Years Exams|1 Videos

  • FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 7: Subjective Type Questions|1 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^2 \ a n d \ g(x)=sinx for all x in R . Then the set of all x satisfying (fogogof)(x)=(gogof)(x),w h e r e (fog)(x)=f(g(x)), is

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

The function f(x)=tanx is discontinuous on the set {npi; n in Z} (b) {2npin in Z} {(2n+1)pi/2: n in Z} (d) {(npi)/2: n in Z}

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

General solution for |sinx|=cosx is (a) 2npi+pi/4,\ n in I (b) 2npi+-pi/4, n in 1 (c) npi+pi/4,\ n in 1 (d) none of these

The general solution of cosxcos6x=-1 is (a) x=(2n+1)pi,n in Z (b) x=2npi,n in Z (c) x=npi,n in Z (d) none of these

Let tanx-tan^2x >0 and |2sinx| npi,n in Z (b) x > npi-pi/6,n in Z x

The general solution of the equation sin^(100)x-cos^(100)x=1 is (a) 2npi+pi/3,n in I (b) n pi+pi/2,n in I (c) npi+pi/4,n in I (d) 2npi=pi/3,n in I

The roots of the equation cot x-cosx=1-cot xcos x are (1) npi+pi/4,n in I (2) 2npi+pi/4,n in I (3) 2npi+-pi or npi+pi/4,n in I (4) 2npi+pi or (4n+1)pi/4,n in I (5) npi,n in I

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  2. The function f:[0,3]vec[1, 29], defined by f(x)=2x^3-15 x^2+36 x+1, is...

    Text Solution

    |

  3. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

  4. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  5. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  6. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  7. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  8. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  9. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  10. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

    Text Solution

    |

  11. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  12. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  13. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  14. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  15. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  16. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  17. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |

  18. Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x)...

    Text Solution

    |

  19. Let g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0. Then for all...

    Text Solution

    |

  20. The domain of definition of the function f(x) given by the equation 2^...

    Text Solution

    |