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Question

If f colon left square bracket 0 comma 1 right square bracket not stretchy rightwards arrow left square bracket negative 1 comma 3 right square bracket defined by f left parenthesis x right parenthesis equals x squared plus x plus 1 text , then  end text f text  is  end text

  1. a function
  2. one one
  3. onto
  4. one one onto

hintHint:

In this question, we have to find the type of function if f left parenthesis x right parenthesis equals vertical line x minus 1 vertical line plus vertical line x minus 2 vertical line plus vertical line x minus 3 vertical line comma f colon left square bracket 2 comma 3 right square bracket not stretchy rightwards arrow R A function f colon A rightwards arrow B is said to be one-one if different elements of A have different images in B, a function f colon A rightwards arrow B is said to be onto if for all y element of B, there exists x element of A such that f (x) = y.

The correct answer is: one one


    w e space h a v e comma f space colon open square brackets 0 comma 1 close square brackets rightwards arrow open square brackets negative 1 comma 3 close square brackets
f left parenthesis x right parenthesis equals x squared plus x plus 1
T h e n comma space f left parenthesis x subscript 1 right parenthesis equals f left parenthesis x subscript 2 right parenthesis
rightwards double arrow x subscript 1 squared plus x subscript 1 plus 1 equals x subscript 2 squared plus x subscript 2 plus 1
rightwards double arrow x subscript 1 squared minus x subscript 2 squared plus x subscript 1 minus x subscript 2 equals 0
rightwards double arrow left parenthesis x subscript 1 minus x subscript 2 right parenthesis left parenthesis x subscript 1 plus x subscript 2 plus 1 right parenthesis equals 0
A s space x subscript 1 plus x subscript 2 plus 1 not equal to 0
rightwards double arrow x subscript 1 equals x subscript 2
S o comma space f space i s space o n e minus space o n e.
C l e a r l y comma space f left parenthesis x right parenthesis equals x squared plus x plus 1 greater or equal than 1 space f o r space a l l space x colon left square bracket 0 comma 1 right square bracket
S o comma space f left parenthesis x right parenthesis space d o e s space n o t space a s s u m e space v a l u e s space minus 1 space a n d space 0.
T h u s comma space f u n c t i o n space i s space n o t space o n t o.

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