Home
Class 12
MATHS
If f:RtoR,g:RtoRandg(x)=x+3and(fog)(x)=(...

If `f:RtoR,g:RtoRandg(x)=x+3and(fog)(x)=(x+3)^(2)`, then what is the value of `f(-3)`?

A

-9

B

0

C

9

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Given `fog(x)=(x+3)^(2)andg(x)=x+3`
`fog(x)=(x+3)^(2)impliesf[g(x)]=(x+3)^(2)`
`impliesf[x+3]x=(x+3)^(2)(becauseg(x)=x+3)`
`impliesf(x)=x^(2)`
Hence, `f(-3)=(-3)^(2)=9`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    NDA PREVIOUS YEARS|Exercise MCQs|119 Videos

  • HEIGHT & DISTANCE

    NDA PREVIOUS YEARS|Exercise Math|45 Videos

Similar Questions

Explore conceptually related problems

If f:RtoR^(+) such that f(x)=(1//3)^(x) , the what is the value of f^(-1)(x) ?

If f:R rarr R,g:R rarr R defined as f(x)=sin x and g(x)=x^(2), then find the value of (gof)(x) and (fog)(x) and also prove that gof f= fog.

If f(x)=x^(2),g(x)=2^x and (fog)(x)=(gof)(x), then the values of x are

If f(x)=x^(2),g(x)=2^x and (fog)(x)=(gof)(x) , then the values of x are

If f: R->R , g: R->R are given by f(x)=(x+1)^2 and g(x)=x^2+1 , then write the value of fog\ (-3) .

If f:R to R, f(x) =x^(2)+2x -3 and g:R to R, g(x) =3x-4 then the value of fog(x) is :

If f(x)=3x-2 and g(x)=x^(2) , then (fog)(x)= . . .

NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. The function f(x)=e^(x),x""inR is

    Text Solution

    |

  2. What is the value of lim(xtooo) ((x+6)/(x+1))^(x+4)

    Text Solution

    |

  3. If f:RtoR,g:RtoRandg(x)=x+3and(fog)(x)=(x+3)^(2), then what is the val...

    Text Solution

    |

  4. What is the value of lim(xto1) ((x-1)^(2))/(|x-1|) ?

    Text Solution

    |

  5. A is associated with

    Text Solution

    |

  6. B is associated with

    Text Solution

    |

  7. C is associated with

    Text Solution

    |

  8. Consider the following statements 1. Every function has a primitive ...

    Text Solution

    |

  9. The function f(x)=(x)/(x^(2)+1) from R to R is

    Text Solution

    |

  10. The function f(x)=cosec x is

    Text Solution

    |

  11. Consider the following statements: I. f(x)=|x-3| is continuous at x=...

    Text Solution

    |

  12. Consider the function f:Rto{0,1} such that f(x)={{:(1","if ,x" is ra...

    Text Solution

    |

  13. What is the value of lim(xto0) (cos(ax)-cos(bx))/(x^(2))

    Text Solution

    |

  14. If f(x)=2x+7andg(x)=x^(2)+7,x""inR, then what are values of x for whic...

    Text Solution

    |

  15. What is lim(xto0) (a^(x)-b^(x))/(x) equal to?

    Text Solution

    |

  16. If the function f(x)=(x(x-2))/(x^(2)-4),xnepm2 is continuous at x=...

    Text Solution

    |

  17. At how many points is the fucntion f(x)=[x] discontinuous?

    Text Solution

    |

  18. If f(x)=(2)/(3)x+(3)/(2),x""inR, then what is f^(-1)(x) equal to ?

    Text Solution

    |

  19. What is lim(xtooo) (sqrt(a^(2)x^(2)ax+1)sqrt(a^(2)x^(2)+1)) equal to?

    Text Solution

    |

  20. What is the value of k for which the following fucntion f(x) is contin...

    Text Solution

    |