Pertanyaan

Jika diketahui ( g ∘ f ) ( x ) = x 2 + 2 x dan f ( x ) = 3 x − 1 , maka g ( x ) adalah …

Jika diketahui $(g \circ f) (x) = x^{2} + 2 x$ dan $f (x) = 3 x - 1$ , maka $g (x)$ adalah $\dots$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

.

$begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x squared plus 8 x plus 7 over denominator 9 end fraction end style$ .

Pembahasan

dan , maka Jadi, .

dan , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell x squared plus 2 x end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell x squared plus 2 x end cell row cell g open parentheses 3 x minus 1 close parentheses end cell equals cell x squared plus 2 x end cell row cell misal space 3 x minus 1 end cell equals cell a comma space maka end cell row cell 3 x end cell equals cell a plus 1 end cell row x equals cell fraction numerator a plus 1 over denominator 3 end fraction comma space sehingga end cell row cell g left parenthesis a right parenthesis end cell equals cell open parentheses fraction numerator a plus 1 over denominator 3 end fraction close parentheses squared plus 2 open parentheses fraction numerator a plus 1 over denominator 3 end fraction close parentheses end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 2 a plus 1 over denominator 9 end fraction plus fraction numerator 2 a plus 2 over denominator 3 end fraction end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 2 a plus 1 over denominator 9 end fraction plus fraction numerator 6 a plus 6 over denominator 9 end fraction end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 8 a plus 7 over denominator 9 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x squared plus 8 x plus 7 over denominator 9 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x squared plus 8 x plus 7 over denominator 9 end fraction end style$ .