Home
Class 12
MATHS
Check the injectivity of the following f...

Check the injectivity of the following function f: `R rarr R` is given by f(x) = `x^(3)`

Promotional Banner

Topper's Solved these Questions

  • INTEGRATION AREA UNDER PLANE CURVES DIFFERENTIAL EQUATION

    USHA PUBLICATION|Exercise EXERCISE|89 Videos

Similar Questions

Explore conceptually related problems

Check which of the following function is onto and into. (i) f :X rarr Y, given by f(x) = 3x, where X = {0, 1, 2 and Y = {0,3,6). (ii) f: Z rarr Z, given by f(x) = 3x + 2, (Z = set of integers).

Prove that the greatest integer function f:R rarr R, given by f(x) = [x] is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Let R be the set of all non -zero real numbers. Then show that f: R rarr R given by f(x) = (1)/(x) is one- one and onto.

Find the composition fog and gof and test whether fog = gof when f and g are functions or R given by f(x) = g(x)=(1-x^3)^(1/3)

Write fog if f:R rarr R and g: R rarr R is given by f(x) = | x| and g(x) = |5x - 2|.

Show that the function f: R rarr R given by f(x) = {{:(1,"if" x gt0),(0, "if" x=0),(-1, "if" x lt 0):} is not one - one

State whether the function f : R rarr R, defined by f(x) = 3 - 4x is onto or not.

If f: R rarr R is defined by f(x) = 3x + 2 define f (f (x))

If the function'f : R rarr R is given by f(x) = x^(2) +2 and g:R rarr R is given by g(x) = (x)/(x-1), x ne 1 then find fog and gof and hence find fog (2) and gof (-3) .

USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. Fill in the blanks : The derivative of abs(2x-5) when xlt5/2 is

    Text Solution

    |

  2. Give an example of a function which is neither one-one nor onto

    Text Solution

    |

  3. Check the injectivity of the following function f: R rarr R is given b...

    Text Solution

    |

  4. What is the maximum value of sinx cosx for x in(pi/6,pi/2)?

    Text Solution

    |

  5. Find the extreme points of the function y= x+1/x.

    Text Solution

    |

  6. Does the. normal at any point on a circle passes through the centre of...

    Text Solution

    |

  7. Examine the continuity of the following functions at the indicated poi...

    Text Solution

    |

  8. examine the contiunity of the following functions at indicated points ...

    Text Solution

    |

  9. Examine the contiunity of the following functions at the indicated poi...

    Text Solution

    |

  10. Examine the continuity of the following functions at indicated points....

    Text Solution

    |

  11. Examine the contiunity of the the following functions at indicated poi...

    Text Solution

    |

  12. Find the derivative of the following functions from definition sqrtx c...

    Text Solution

    |

  13. Find the derivative of the following functions from definition sin^2x.

    Text Solution

    |

  14. Find the derivative of the following functions from definition sqrt(ta...

    Text Solution

    |

  15. f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

    Text Solution

    |

  16. Test the differentiability of the following functions f(x)=x/(1+absx)a...

    Text Solution

    |

  17. If y = tan^-1((acosx-bsinx)/(bcosx+asinx)), then find (dy)/(dx)

    Text Solution

    |

  18. If y = tan^-1(secx+tanx), then find (dy)/(dx).

    Text Solution

    |

  19. Find (dy)/(dx), if y=sin^-1((sqrt(1+x)+sqrt(1-x))/2), -1ltxlt1

    Text Solution

    |

  20. Find (dy)/(dx), if x=sqrt(sin2u) and y=sqrt(cos2u)

    Text Solution

    |