Materi : Fungsi dan Relasi, Fungsi Komposisi
f(x) = 1/x
g(x) = 2/( x - 1 )
___________/
( g • f )(x) = g(f(x)) = g(1/x)
= 2/( 1/x - 1 )
= 2/( 1/x - x/x )
= 2 ÷ ( 1 - x )/x
= 2 . x/( 1 - x )
= 2x/( 1 - x )
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
[tex] \begin{align}(g\circ f)(x) &= g(f(x)) \\ &= g\left(\dfrac{1}{x}\right) \\ &= \dfrac{2}{\frac{1}{x}-1} \\ &= \frac{2}{\frac{1}{x}-\frac{x}{x}} \\ &= \frac{2}{\frac{1-x}{x}} \\ &= 2 \cdot \dfrac{x}{1-x} \\ &= \dfrac{2x}{1-x} \end{align} [/tex]
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2025 KUDO.TIPS - All rights reserved.
Materi : Fungsi dan Relasi, Fungsi Komposisi
f(x) = 1/x
g(x) = 2/( x - 1 )
___________/
( g • f )(x) = g(f(x)) = g(1/x)
= 2/( 1/x - 1 )
= 2/( 1/x - x/x )
= 2 ÷ ( 1 - x )/x
= 2 . x/( 1 - x )
= 2x/( 1 - x )
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
Verified answer
[tex] \begin{align}(g\circ f)(x) &= g(f(x)) \\ &= g\left(\dfrac{1}{x}\right) \\ &= \dfrac{2}{\frac{1}{x}-1} \\ &= \frac{2}{\frac{1}{x}-\frac{x}{x}} \\ &= \frac{2}{\frac{1-x}{x}} \\ &= 2 \cdot \dfrac{x}{1-x} \\ &= \dfrac{2x}{1-x} \end{align} [/tex]