Maths-
General
Easy

Question

f left parenthesis x right parenthesis equals x plus square root of x squared end root is a function from R to R, then f left parenthesis x right parenthesis is

  1. Injective
  2. Surjective
  3. Bijective
  4. None of these

The correct answer is: None of these


    Given, f left parenthesis x right parenthesis equals x plus square root of x squared end root
    Since, this function is not defined
    Given, f left parenthesis x right parenthesis equals x cubed minus 1
    Let x subscript 1 comma x subscript 2 element of R
    Now, f open parentheses x subscript 1 close parentheses equals f open parentheses x subscript 2 close parentheses
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow x subscript 1 superscript 3 minus 1 equals x subscript 2 superscript 3 minus 1 end cell row cell not stretchy rightwards double arrow x subscript 1 superscript 3 equals x subscript 2 superscript 3 end cell row cell not stretchy rightwards double arrow x subscript 1 equals x subscript 2 end cell end table
    therefore f left parenthesis x right parenthesis is one-one. Also, it is onto as range of
    Hence, it is a bijection.

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