Question

domain range of f(x)=4/3-x​

Answer 1

GIVEN :-

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

TO FIND :-

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

SOLUTION :-

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

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

$\tt \: 3 - x = 0$

$\implies \tt \: x = 3$

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

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

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

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

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

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

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

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

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

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