Home
Class 12
MATHS
Let f: R->R be any function. Also g: R->...

Let `f: R->R` be any function. Also `g: R->R` is defined by `g(x)=|f(x)|` for all `xdot` Then `g` is
a. Onto if `f` is onto b. One-one if `f` is one-one c. Continuous if `f` is continuous d. None of these

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos
  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

Let f : R rarr R be any function. Define g : R rarr R by g(x)=|f(x)| for all x. Then g is:

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 the function f:R to R be defined by f(x)=x+sinx for all x in R. Then f is -

Let f,g: R-R be two functions defined as f(x)=|x|+x and g(x)=|x|-x , for all x Then find fog and gof.

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

Show f:R rarr R defined by f(x)= x^2 + x for all x in R is many one.

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

Let f:R to R be defined by f(x)=x|x| , then the function f is -

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot Then f is (a)one-to-one and onto (b)one-to-one but not onto (c)onto but not-one-to-one (d)neither one-to-one nor onto

Let f:R to R be defined by f(x)=x^(2) and g:R to R be defined by g(x)=x+5 . Then , (gof)(x) is equal to -

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. For which of the following functions f(0) exists such that f(x) is con...

    Text Solution

    |

  2. Determine the values of a so that the funtion is continuous at x=1. f...

    Text Solution

    |

  3. Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| fo...

    Text Solution

    |

  4. Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-...

    Text Solution

    |

  5. The function f:R→R satisfies f(x^2 ).f ′′ (x)=f ′ (x).f ′ (x^...

    Text Solution

    |

  6. The second derivative of a single valued function parametrically re...

    Text Solution

    |

  7. If lim(x→0) ​ (x^asin^b x)/(sin(x^c)), where a , b , c in ...

    Text Solution

    |

  8. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2)...

    Text Solution

    |

  9. If f(1)=3,f^(prime)(1)=2,f ^(' ')(1)=4,t h e n(f^(-1))^(' ')(3)= a. 1...

    Text Solution

    |

  10. If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

    Text Solution

    |

  11. If R=([1+((dy)/(dx))^2]^(3//2))/((d^2y)/(dx2)) , thenR^(2//3) can be p...

    Text Solution

    |

  12. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2) is (a)3/2 (b) 3/(4t) (c) 3/(2t) (...

    Text Solution

    |

  13. The function f(x)=(x^3)/8-sinpix+4 in [-4,4] does not take the value a...

    Text Solution

    |

  14. If f(x)={(|x|-3 when x < 1), and (|x-2|+a , when x >= 1) & g(x)={2...

    Text Solution

    |

  15. The number of points of discontinuity of f(x)=[2x]^(2)-{2x}^(2) (where...

    Text Solution

    |

  16. The number of points of discontinuity of g(x)=f(f(x)) where f(x) is ...

    Text Solution

    |

  17. Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b...

    Text Solution

    |

  18. If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is cont...

    Text Solution

    |

  19. Let f(x)=(lim)(n rarr oo)sum(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (...

    Text Solution

    |

  20. Let f(x)={lim(n->oo)(a x(x-1)(cot((pix)/4))^n+(p x^2+2))/((cot((pix)/...

    Text Solution

    |