Question

$ f ( x )$ and $g ( x )$ are linear functions such that for all $x , f ( g ( x ))$ ) and $g ( f ( x ))$ are identity functions, if $f (0)=4, g (5)=17$ and $f (136)=4 k$. Then find the value of $k$.

Answer 1

$ f ( x )= mx +4 $
$g ( x )= m ^{\prime}( x -5)+17 $
$g ( f ( x ))= m ^{\prime}[( mx +4)-5]+17= x$
$\Theta \text { Identify function } $
$\Rightarrow m =\frac{1}{17}, m ^{\prime}=17 $
$\Rightarrow f ( x )=\frac{1}{17} x +4$
$f (136)=12=4 k \Rightarrow k =3$