Question

f(x)=2x-1÷5x-3 find range and domain​

Answer 1

$\large \bf \star \: \: \: {{\underline{ \underline{{Given}}}}} \: \: \: \star \\ \\ \\ \natural \: \: \: \: \tt \: \: \: \tt \: f(x) = \frac{2x - 1}{5x - 3} \\ \\ \\ \\ \large \bf \star \: \: \: {{\underline{ \underline{{ Solution }}}}} \: \: \: \star\\ \\ \\ \sf \: \Box \: \: \: \: { \underline{Domain \: \: of \: \: the \: \: function \: (D_f) : }} \\ \\ \tt \: denominator \: \: can \: \: never \: \: be \: \: zero \: \: for \: \: it \: \: to \: \: be \: \: a \: \: function \\ \tt \: hence, \\ \tt5x - 3 \not = 0 \\ \\ \implies \tt \: x \not = \frac{3}{5} \\ \\ \\ \bf\therefore \: \: \tt \: Function \: \: is \: \: defined \: , \: { \: \forall \: x \: \in \: \: \R - \bigg \{ \frac{3}{5} \bigg\} } \\ \\ \tt \bf \therefore \: \: \: Domain \: \: of \: \: function \: \: \: \R - \bigg \{ \frac{3}{5} \bigg\}\\ \\ \\ \Box \sf \: \: \: \: { \underline{Range \: \: of \: \: the \: \: function \: (R_f) : }} \\ \\ \tt \: We \: \: will \: \: get \: \: any \: \: real \: \: value \: \: of \: \: f(x) \: \: in \: \: its \: \: domain \\ \\ \\ \bf \therefore \: \: \: Range \: \: of \: \: function \: \: \R \\ \\ \\ \\ \large \bf \star \: \: \: {{\underline{ \underline{{Concept \: \: Booster}}}}} \: \: \: \star \\ \\ \\ \tt \: Let's \: \: have \: \: a \: \: look \: \: on \: \: its \: \: Graph \\ \\ \tt \: we \: \: can \: \: see \: \: easily \: \: see \: \: from \: \: its \: \: graph \: \: that \: \: function \: \: is \: \: undefind \: \: at \: \: x = \frac{3}{5} \\ \\ \\ \mathcal{ \small \colorbox{aqua}{@StayHigh}}$