Math, asked by sivaramyam2810, 3 months ago

domain range of f(x)=4/3-x​

Answers

Answered by PharohX
6

GIVEN :-

  •  \tt \: f(x) \: = \:  \frac{4}{3 - x}  \\

TO FIND :-

  •  \tt \: domain \: and \: range \: of \: the \: function

SOLUTION :-

 \bull \tt  \: calculation \:  \: of \:  \: domain -

 \tt \:  \: Taking \: the \: denominator \:equal  \: to \:  \: zero

 \tt \: 3 - x = 0

 \implies \tt \: x = 3

 \tt \: Here \: at \: \:  x  = 3 \: the \: function \: is \: not \: difine

 \green{ \boxed{ \tt \: Hence \: domain \:  = R -  \{3 \}}}

 \bull \tt  \: calculation \:  \: of \:  \: range -

 \tt \: f(x) \: = \:  \frac{4}{3 - x}  \\

 \tt \: Let \:  \:  f(x)=y

  \implies\tt \: y\: = \:  \frac{4}{3 - x}  \\

  \implies\tt \: 3 - x\: = \:  \frac{4}{y}  \\

  \implies\tt \:  x\: = \:3 -   \frac{4}{y}  \\

 \tt \: Here \:  x \: be \:  \: not \: define\:  at \: y   = 0\:

 \green{ \boxed{{ \tt \: Hence \: range \:  = R -  \{0 \}}}}

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