Pertanyaan

Diberikan f ( x ) = x − 4 6 , x  = 4 , dan ( g ∘ f ) ( x ) = x − 4 2 x + 5 , x  = 4 . Tentukan rumus g ( x ) .

Diberikan $f (x) = \frac{6}{x - 4}, x \neq = 4$ , dan $(g \circ f) (x) = \frac{2 x + 5}{x - 4}, x \neq = 4$ . Tentukan rumus $g (x)$ .

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

g ( x ) = 6 13 x + 2 .

g (x) = \frac{13}{6} x + 2

Pembahasan

dan . Misalkan : Substitusikan ke , diperoleh: Dengan demikian, g ( x ) = 6 13 x + 2 .

dan $begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 5 over denominator x minus 4 end fraction comma space x not equal to 4 end cell end table end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 5 over denominator x minus 4 end fraction end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell fraction numerator 2 x plus 5 over denominator x minus 4 end fraction end cell row cell g open parentheses fraction numerator 6 over denominator x minus 4 end fraction close parentheses end cell equals cell fraction numerator 2 x plus 5 over denominator x minus 4 end fraction space space space... space open parentheses 1 close parentheses end cell end table end style$

Misalkan :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 6 over denominator x minus 4 end fraction end cell equals y row 6 equals cell y open parentheses x minus 4 close parentheses end cell row cell 6 over y plus 4 end cell equals x end table end style$

Substitusikan ke , diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell g open parentheses y close parentheses end cell equals cell fraction numerator 2 open parentheses begin display style 6 over y end style plus 4 close parentheses plus 5 over denominator open parentheses begin display style 6 over y end style plus 4 close parentheses minus 4 end fraction end cell row blank equals cell fraction numerator begin display style 12 over y end style plus 8 plus 5 over denominator begin display style 6 over y end style end fraction times y over y end cell row blank equals cell fraction numerator 12 plus 13 y over denominator 6 end fraction end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 13 x over denominator 6 end fraction plus 2 end cell end table end style$

Dengan demikian, $g (x) = \frac{13}{6} x + 2$ .