Home
Class 12
MATHS
Show that the function f: R rarr R , f(x...

Show that the function f: R `rarr` R , f(x)=`x^(4)` is many-one and into.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE ( Short Answer Type Questions ) |9 Videos

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE ( Long Answer Type Questions ) |14 Videos

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU.S TEXTBOOK SOLUTIONS ( Exercise 1 (c))|14 Videos

  • QUESTION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|13 Videos

  • SAMPLE PAPER 1

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|13 Videos

Similar Questions

Explore conceptually related problems

Show that the function f : R rarr R defined as f(x) = x^(2) is neither one-one nor onto.

Show that the function f:N to N given by f(x) =2x , is one-one but not onto.

Let A = { x:x in R ,(-pi)/(2) lt= xlt= (pi)/(2)} and B = (y:y in R , -1 lt= y lt=1} . Show that the function f : A rarr B given by f(x) = sin x is invertible andc hence find f^(-1) .

Show that the function f :R rarr R, given by f(x) = cos x, AA x in R is neither one-one nor onto.

Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neither one-one nor onto.

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

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

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.

Show that a function f:R to R given by f(x)=3x+5 is a bijective.

Show that the function f: N rarr N, given by f(1) f(2)= 1 and f(x) = x - 1 for every x gt 2, is onto but not one-one.

ARIHANT PUBLICATION-RELATIONS AND FUNCTIONS -CHAPTER PRACTICE (Very Short Answer Type Questions )
  1. Let A = {1,2,3,4,…., 15,16} and let R be a relation in A given by R={...

    Text Solution

    |

  2. If the relation R is defined on the set A={1,2,3,4,5} by R={a,b} : |a^...

    Text Solution

    |

  3. State the reason for the relation R in the set {1, 2, 3} given by R ={...

    Text Solution

    |

  4. Show that the function f: R rarr R , f(x)=x^(4) is many-one and into.

    Text Solution

    |

  5. If f(x)=27x^(3) and g(x) =x^(1//3). Then, find gof(x).

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Find gof and fog, if f: R rarr R and g: R rarr R are given by f(x) = c...

    Text Solution

    |

  9. If A= {a,b,c,d) and the function f = {(a,b),(b,d), (c,a), (d,c)}, then...

    Text Solution

    |

  10. If f is an invertible function, defined as f(x)= (3x-4)/(5) then write...

    Text Solution

    |

  11. Let* is a binary operation on the set of all non-zero real numbers, gi...

    Text Solution

    |

  12. If the binary operation on the set of integers Z, defined by a b= a +3...

    Text Solution

    |

  13. Show that * On Z^(+) defined by a*b = |a-b| is a binary operation or n...

    Text Solution

    |

  14. Show that * On R defined by a*b = a +4b^(2) is a binary operation or n...

    Text Solution

    |

  15. For each binary operation defined below, determine whether * is the co...

    Text Solution

    |

  16. For each binary operation defined below, determine whether * is the co...

    Text Solution

    |

  17. Prove that for binary operation defined on R such that ab=a+4b^(2) is ...

    Text Solution

    |

  18. For each binary operation * defined below, determine the identity elem...

    Text Solution

    |

  19. For each binary operation * defined below, determine the identity elem...

    Text Solution

    |