Home
Class 12
MATHS
consider the function f:R rarr R,f(x)=(x...

consider the function `f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4)`
f(x) is

A

unbounded function

B

one one function

C

onto function

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
4
`f(X)=(x^(2)-6x+4)/(x^(2)+2x+4)=1-(8x)/(x^(2)+2x+4)`
`f(x)-8((x^(2)+2x+4)-x(2x+2))/((x^(2)+2x+4)^(2)`
`f(X)=0 rarrx2 or -2`
`f(2)=(4-12+4)/(4+4+4)=-4/12=-1/3`
`f(2)=(4+12+4)/(4-4+4)=5`
The graph of y =f(X) is as shown
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Matrix Match Type|11 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Numerical Value Type|24 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|48 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). f(3) is

If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let A={x in R:x" is not a positive integer "} define a function f:AtoR" such that "f(x)=(2x)/(x-1) . Then f is

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

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

If f: RR^(+) rarr RR ^(+) is a polynomial function satisfying the functional equation f{f(x)}=6x-f(x) , then f(17) is equal to ___

Determine all functions f : R rarr R satisfying f(x-f(y)) = f(f(y)) + xf(y) + f(x) - 1 AA x, y in R

Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-

The function f:R->[-1/2,1/2] defined as f(x)=x/(1+x^2) is

CENGAGE PUBLICATION-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Linked comprehension type
  1. consider the function f(X) =x+cosx which of the following is not tru...

    Text Solution

    |

  2. consider the function f(X) =x+cosx -a values of a which f(X) =0 has ...

    Text Solution

    |

  3. consider the function f(X) =x+cosx -a values of a for which f(X) =0 ...

    Text Solution

    |

  4. consider the function f(X) =3x^(4)+4x^(3)-12x^(2) Y= f(X) increase i...

    Text Solution

    |

  5. consider the function f(X) =3x^(4)+4x^(3)-12x^(2) The range of the f...

    Text Solution

    |

  6. consider the function f(X) =3x^(4)+4x^(3)-12x^(2) The range of value...

    Text Solution

    |

  7. consider the function f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4) f(x)...

    Text Solution

    |

  8. consider the function f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4) whic...

    Text Solution

    |

  9. consider the function f:R rarr R,f(x)=(x^(2)-6x+4)/(x^(2)+2x+4) Rang...

    Text Solution

    |

  10. Consider a polynomial y = P(x) of the least degree passing through A(-...

    Text Solution

    |

  11. Consider a polynomial y = P(x) of the least degree passing through A(-...

    Text Solution

    |

  12. Consider a polynomial y = P(x) of the least degree passing through A(-...

    Text Solution

    |

  13. Let f(X) be real valued continous funcion on R defined as f(X) =x^(2)e...

    Text Solution

    |

  14. Let f(x) be real valued continous funcion on R defined as f(x) =x^(2)e...

    Text Solution

    |

  15. Let f(x) be real valued continous funcion on R defined as f(x) =x^(2)e...

    Text Solution

    |

  16. P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p...

    Text Solution

    |

  17. P(x) be a polynomial of degree 3 satisfying P(-1) =10 , P(1) =-6 and p...

    Text Solution

    |

  18. The graph of y =g(x) =f(X) is as shown in the following figure analyse...

    Text Solution

    |

  19. The graph of y =g(x) =f(X) is as shown in the following figure analyse...

    Text Solution

    |

  20. The graph of y =g(x) =f(X) is as shown in the following figure analyse...

    Text Solution

    |