Home
Class 12
MATHS
The function f:(-oo,-1)vec(0, e^5) defin...

The function `f:(-oo,-1)vec(0, e^5)` defined by `f(x)=e^x^(3-3x+2)` is many one and onto many one and into one-one and onto one-one and into

A

many-one and onto

B

many-one and into

C

one-one and onto

D

one-one and into

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=e^(x^(3)-3x+2)`
Let `g(x)=x^(3)-3x+2,`
` g'(x)=3x^(2)-3=3(x^(2)-1)`
` ge 0 " for " x in (-oo,-1]`
Therefore, `f(x)` is increasing function. Hence, `f(x)` is one-one.
Now, the range of `f(x)" is "(0,e^(4)].`
But co-domain is `(0,e^(5)].`
Hence, `f(x)` is an into function.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|32 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.15|8 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|31 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

The function f:(-oo,-1)rarr(0,e^(5)) defined by f(x)=e^(x^(3)-3x+2) is (a)many one and onto (b)many one and into (c)one-one and onto (d)one-one and into

The function f: R->R defined by f(x)=2^x+2^(|x|) is (a) one-one and onto (b) many-one and onto (c) one-one and into (d) many-one and into

The function f: R->R defined by f(x)=6^x+6^(|x|) is (a) one-one and onto (b) many one and onto (c) one-one and into (d) many one and into

Let f:R^(+)rarr{-1,0,1} defined by f(x)=sgn(x-x^(4)+x^(7)-x^(8)-1) where sgn denotes signum function then f(x) is (1) many- one and onto (2) many-one and into one-one and onto (4) one- one and into

The function f:[-(1)/(2),0]rarr B, defined by f(x)=cos^(-1)(4x^(2)+3x) is both one-one and onto if

The function f::[0,3]rarr[1,29], defined by f(x)=2x^(3)-15x^(2)+36x+1, is (a) one-one and onto (b) onto but not one-one (c) one-one but not onto (d) neither one-one nor onto

f: N rarr N, where f(x)=x-(-1)^(x) .Then f is: (a)one-one and into (b)many-one and into (c)one-one and onto (d)many-one and onto

The function f:[2,oo)rarr Y defined by f(x)=x^(2)-4x+5 is both one-one and onto if

Let f:R rarr R, be defined as f(x)=e^(x^(2))+cos x, then is (a) one-one and onto (b) one-one and into ( c) many-one and onto (d) many-one and into

the function f : R rarr [ -1,1 ] defined by f(x) = cos x is (a) both one-one and onto (b) not one-one, but onto (c) one-one, but not onto (d) neither one-one, nor onto

CENGAGE-RELATIONS AND FUNCTIONS-Exercise (Single)
  1. f:N to N, where f(x)=x-(-1)^(x), Then f is

    Text Solution

    |

  2. If S be the set of all triangles and f : S -> R^+, f(Delta) = Area of...

    Text Solution

    |

  3. The function f:(-oo,-1)vec(0, e^5) defined by f(x)=e^x^(3-3x+2) is man...

    Text Solution

    |

  4. Let f:N->N be defined by f(x)=x^2+x+1,x in N. Then is f is

    Text Solution

    |

  5. Let X={a1, a2, ,a6}a n dY={b1, b2,b3}dot The number of functions f fro...

    Text Solution

    |

  6. Which of the following functions is an injective (one-one) function in...

    Text Solution

    |

  7. Given the function f(x)=(a^x+a^(-x))/2(w h e r ea >2)dotT h e nf(x+y)+...

    Text Solution

    |

  8. If f(x)=cos (logx), then f(x)f(y)-1/2[f(x/y)+f(xy)]=

    Text Solution

    |

  9. The domain of the function f(x)=(1)/(sqrt(""^(10)C(x-1)-3xx""^(10)C(x)...

    Text Solution

    |

  10. The domain of the function f(x)=(sin^(-1)(3-x))/("In"(|x|-2)) is

    Text Solution

    |

  11. The domain of f(x)=(log(2)(x+3))/(x^(2)+3x+2) is

    Text Solution

    |

  12. The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the gre...

    Text Solution

    |

  13. The domain of the function f(x)=log(3+x)(x^(2)-1) is

    Text Solution

    |

  14. Domain of the function, f(x)=[log10 ((5x-x^2)/4)]^(1/2) is

    Text Solution

    |

  15. The domain of f(x)=log|logx| is

    Text Solution

    |

  16. If x^3f(x)=sqrt(1+cos2x)+|f(x)|, (-3pi)/4ltxlt(-pi) /2 and f(x)=(alpha...

    Text Solution

    |

  17. The function f(x)=(sec^(-1)x)/(sqrt(x)-[x]), where [x] denotes the gre...

    Text Solution

    |

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

    Text Solution

    |

  19. The domain of f(x)=cos^(-1)((2-|x|)/4)+[l log(3-x)]^1 is [-2,6] (b...

    Text Solution

    |

  20. The domain of the function f(x)=sqrt(log((1)/(|sinx|)))

    Text Solution

    |