Pertanyaan

Diketahui fungsi f ( x − 2 ) = x − 1 3 x dan g ( x + 2 ) = 2 x − 3 . Tentukanlah : c. ( f ∘ g ) ( x )

Diketahui fungsi $f (x - 2) = \frac{3 x}{x - 1}$ dan $g (x + 2) = 2 x - 3$ . Tentukanlah :

c. $(f \circ g) (x)$

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Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 6 x minus 15 over denominator 2 x minus 6 end fraction end style$ .

Pembahasan

Diketahui fungsi dan . Menentukan : Menentukan : Maka : Dengan demikian .

Diketahui fungsi $begin mathsize 14px style f open parentheses x minus 2 close parentheses equals fraction numerator 3 x over denominator x minus 1 end fraction end style$ dan .

Menentukan :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px 2px 2px end attributes row misalkan colon blank row cell x minus 2 end cell equals t row x equals cell t plus 2 end cell row blank blank blank row cell f open parentheses x minus 2 close parentheses end cell equals cell fraction numerator 3 x over denominator x minus 1 end fraction end cell row cell f open parentheses t close parentheses end cell equals cell fraction numerator 3 open parentheses t plus 2 close parentheses over denominator t plus 2 minus 1 end fraction end cell row blank equals cell fraction numerator 3 t plus 6 over denominator t plus 1 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 6 over denominator x plus 1 end fraction end cell end table end style$

Menentukan :

Maka :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator 3 open parentheses g open parentheses x close parentheses close parentheses plus 6 over denominator g open parentheses x close parentheses plus 1 end fraction end cell row blank equals cell fraction numerator 3 open parentheses 2 x minus 7 close parentheses plus 6 over denominator 2 x minus 7 plus 1 end fraction end cell row blank equals cell fraction numerator 6 x minus 21 plus 6 over denominator 2 x minus 6 end fraction end cell row blank equals cell fraction numerator 6 x minus 15 over denominator 2 x minus 6 end fraction end cell end table end style$

Dengan demikian $begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals fraction numerator 6 x minus 15 over denominator 2 x minus 6 end fraction end style$ .