Home
Class 12
MATHS
Let f(x)=x+2|x+1|+x-1|dotIff(x)=k has ex...

Let `f(x)=x+2|x+1|+x-1|dotIff(x)=k` has exactly one real solution, then the value of `k` is 3 (b) 0 (c) 1 (d) 2

A

3

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(x)=x+2|x+1|+2|x-1|`
`={(x-2(x+1)-2(x-1)",", x lt -1),(x+2(x+1)-2(x-1)",", -1 le x le 1),(x+2(x+1)+2(x-1)",", x gt 1):}`
`={(-3x",", x lt -1),(x+4",", -1 le x le 1),(5x",", x gt 1):}`
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

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

Let f(x)=x + 2|x+1|+2| x-1| . Find the values of k if f(x)=k (i) has exactly one real solution, (ii) has two negative solutions, (iii) has two solutions of opposite sign.

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,npi] , then value/values of n is/are (n in N) 5 (b) 3 (c) 4 (d) 6

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

The number of real solutions of the (log)_(0. 5)(x)=|x| is (a) 1 (b) 2 (c) 0 (d) none of these

If f(x)={(|x|-3 when x = 1) & g(x)={2-|x| when x = 2 . if h(x)=f(x)+g(x) is discontinuous at exactly one point, then - (a). a=-3, b=0 (b). a=-3, b=-1 (c) a=2, b=1 (d) a=0, b=1

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are a. -1,2 b. 1,2 c. 0,1 d. -1,1

Let h(x)=|k x+5| ,then domainof f(x) be [-5,7], the domain of f(h(x)) be [-6,1] ,and the range of h(x) be the same as the domain of f(x). Then the value of k is. (a)1 (b) 2 (c) 3 (d) 4

If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then one of the values of k is (a) 1/8 (b) 8 (c) 4 (d) 1/4

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Number of integral values of k for which the equation 4 cos^(-1)(-|x|)...

    Text Solution

    |

  2. If f(x) is a real=valued function defined as f(x)=1N(1-sinx), then the...

    Text Solution

    |

  3. Let f(x)=x+2|x+1|+x-1|dotIff(x)=k has exactly one real solution, then ...

    Text Solution

    |

  4. The number of solutions of 2cosx=|sinx|,0lt=xlt=4pi, is (a) 0 (b) 2 ...

    Text Solution

    |

  5. Given that f(x)=5x^2−8x,g(x)=x^2−5x−24 . Find ( f/g)(x)

    Text Solution

    |

  6. If log(4)((2f(x))/(1-f(x)))=x, " then "(f(2010)+f(-2009)) is equal to

    Text Solution

    |

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

    Text Solution

    |

  8. Let f : R rarr[-1,oo] and f(x)= ln([|sin 2 x|+|cos 2 x|]) (where[.] is...

    Text Solution

    |

  9. If f: R ->Nuu{0}, where f (area of triangle joining points P(5,0),Q(8,...

    Text Solution

    |

  10. The domain of the function f(x)=(log)e{(log)(|sinx|)(x^2-8x+23)-{3/((l...

    Text Solution

    |

  11. Let f(x)=sgn(cot^(-1)x)+tan((pi)/(2)[x]), where [x] is the greatest in...

    Text Solution

    |

  12. f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then

    Text Solution

    |

  13. If the following functions are defined from [-1,1]to[-1,1], select tho...

    Text Solution

    |

  14. Let f(x)={x^2-4x+3,x<3x-4,xgeq3 a n dg(x)={x-3,x<4x^2+2x+2,xgeq4 the...

    Text Solution

    |

  15. Let f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi] and g(x)=max{1,|x-1|} x in R...

    Text Solution

    |

  16. If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,...

    Text Solution

    |

  17. Consider the real-valued function satisfying 2f(sinx)+f(cosx)=xdot the...

    Text Solution

    |

  18. If f: R^+vecR^+ is a polynomial function satisfying the functional equ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |