Question

find the domain of f of x equal to log of x square minus4xplus3
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Answer 1

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GiveN :

$\mapsto \sf \: f(x) = log( {x}^{2} - 4x + 3)$

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SolutioN :

$\tt \: \underline{Domain \: \: of \: \: function \: ( D_f) \: :}$

$\sf \: ( {x}^{2} - 4x + 3) \: \: should \: \: always \: \: be \: \: greater \: \: than \: \: 0$

$\sf \: for \: \: it \: \: to \: \: be \: \: a \: \: function$

$\mapsto\sf \: {( {x}^{2} - 4x + 3)} > 0$

$\implies \: \sf(x - 3)(x - 1) > 0$

$\implies { { { \sf \: x \in \: ( \: 1 \: , \: \infty \: ) - \{3 \}}}}$

$\mapsto \underline{ \boxed{ \sf{D_f = ( \: 1 \: , \: \infty \: ) - \{3 \}}}}$

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$\tt \: \underline{ Range\: \: of \: \: function \: ( R_f) \: :}$

$\sf \: Range \: \: of \: \: function \: \: log \: \: is \: \: always \: \: \: R {}^+ + \{0 \}$

$\mapsto \underline{ \boxed{ \sf{R_f =R {}^+ + \{0 \} }}}$

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ConcepT BoosteR :

→ For better understanding we need to learn the Graphical representation of functions

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HOPE THIS IS HELPFUL...