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.

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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f ( x )= mx +4 g ( x )= m prime( x -5)+17 g ( f ( x ))= m prime[( mx +4)-5]+17= x Θ text Identify function ⇒ m =(1/17), m prime=17 ⇒ f ( x )=(1/17) x +4 f (136)=12=4 k ⇒ k =3

Q. $f (x)$ 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 $k$ .

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

Q. 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)=4k. Then find the value of k.

f(x)=mx+4 g(x)=m′(x−5)+17 g(f(x))=m′[(mx+4)−5]+17=x Θ Identify function ⇒m=171​,m′=17 ⇒f(x)=171​x+4 f(136)=12=4k⇒k=3

Q. $f (x)$ 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 $k$ .

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