Pertanyaan

Diketahui f ( x ) = 3 x + 7 dan h ( x ) = x + 1 x − 3 , x  = 1 , dan ( g ∘ f ) ( x ) = 3 x + 9 3 x + 7 , komposisi fungsi ( g ∘ h ) ( x ) = ...

Diketahui $f (x) = 3 x + 7$ dan $h (x) = \frac{x - 3}{x + 1}, x \neq = 1$ , dan $(g \circ f) (x) = \frac{3 x + 7}{3 x + 9}$ , komposisi fungsi $(g \circ h) (x) = ...$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style open parentheses g ring operator h close parentheses open parentheses x close parentheses equals fraction numerator x minus 3 over denominator x squared plus 3 x plus 2 end fraction end style$

Pembahasan

Jadi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row cell fraction numerator 3 x plus 7 over denominator 3 x plus 9 end fraction end cell equals cell g open parentheses 3 x plus 7 close parentheses end cell row cell fraction numerator open parentheses 3 x plus 7 close parentheses over denominator open parentheses 3 x plus 7 close parentheses plus 2 end fraction end cell equals cell g open parentheses 3 x plus 7 close parentheses end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator x over denominator x plus 2 end fraction end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h close parentheses open parentheses x close parentheses end cell equals cell g open parentheses h open parentheses x close parentheses close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell g open parentheses fraction numerator x minus 3 over denominator x plus 1 end fraction close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell fraction numerator begin display style fraction numerator x minus 3 over denominator x plus 1 end fraction end style over denominator x plus 2 end fraction end cell row cell space space space space space space space space space space space space space space space space end cell equals cell fraction numerator x minus 3 over denominator x plus 1 end fraction times fraction numerator 1 over denominator x plus 2 end fraction end cell row cell space space space space space space space space space space space space space space space space end cell equals cell fraction numerator x minus 3 over denominator x squared plus 3 x plus 2 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style open parentheses g ring operator h close parentheses open parentheses x close parentheses equals fraction numerator x minus 3 over denominator x squared plus 3 x plus 2 end fraction end style$