CBSE Class 11-science Answered

why can't the domain of a function be 0..when 0 is real number????..please explain giving examples of both linear and rational functions..also please explain why can't the range be 0????..

Asked by shailesh arlekar | 15 Mar, 2016, 07:40: PM

Expert Answer

begin mathsize 12px style Both space domain space set space and space range space set space of space straight a space function space CAN space have space apostrophe 0 apostrophe. For space example space straight f left parenthesis straight x right parenthesis equals straight x space has space domain space as space the space entire space real space number space set space which space INCLUDES space apostrophe 0 apostrophe. However space if space we space have space straight a space function space straight g left parenthesis straight x right parenthesis equals 1 over straight x comma space this space function space is space NOT space defined space for space straight x equals 0 comma because space when space straight x equals 0 comma space we space get space straight a space fraction space with space apostrophe 0 apostrophe space as space the space denominator. straight A space fraction space with space apostrophe 0 apostrophe space as space the space denominator space is space not space defined. Similarly space range space of space straight a space function space CAN space be space zero. space It space depends space on space the space function. For space example space the space function comma space straight f left parenthesis straight x right parenthesis equals straight x space has space straight a space value space of space apostrophe 0 apostrophe space when space straight x space is space apostrophe 0 apostrophe. Hence comma space range space can space be space apostrophe 0 apostrophe. However comma space if space we space define space straight a space function space straight h left parenthesis straight x right parenthesis equals straight x squared plus 1 comma space then space the space domain space is space set space of space all space real space numbers. The space range space is space set space of space real space numbers space greater space than space or space equal space to space 1. left parenthesis since space straight x squared greater or equal than 0 rightwards double arrow straight x squared plus 1 greater or equal than 1 right parenthesis So space whether space the space domain space set space or space range space set space of space straight a space function space has space apostrophe 0 apostrophe space in space it space or space not comma depends space on space how space the space function space is space defined. In space case space of space rational space function comma space the space expression space in space the space denominator space CAN space NOT space be space zero. So space any space value space of space apostrophe straight x apostrophe comma space that space gives space zero space value space for space the space DENOMINATOR comma space is space excluded space from space the space domain space set. Example colon space straight f left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator 1 plus straight x end fraction. space This space rational space function space has space straight x plus 1 space in space the space denominator. So space if space we space take space straight x equals negative 1 comma space thedenominator space becomes space zero comma space and space the space expression space becomes space undefined. Hence comma space in space this space case comma space the space domain space set space has space the space set space of space all space real space numbers space except space minus 1. Hope space this space clears space your space doubt. end style

Answered by satyajit samal | 16 Mar, 2016, 12:31: PM

CBSE Class 11-science Answered

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