Jika f∘g(x)=3x−4, dan f(x)=2x+6, tentukan nilai dari g(2)!

Pertanyaan

Jika $\style{font-size:14px}{f\circ g(x)=3x-4}$ , dan $\style{font-size:14px}{f(x)=2x+6}$ , tentukan nilai dari $\style{font-size:14px}{g(2)}$ !

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Diketahui dan .

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g left parenthesis x right parenthesis end cell equals cell 3 x minus 4 end cell row cell space f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 3 x minus 4 end cell row cell space 2 g left parenthesis x right parenthesis plus 6 end cell equals cell 3 x minus 4 space end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell 3 x minus 4 minus 6 space end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell 3 x minus 10 end cell row cell space g left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x minus 10 over denominator 2 end fraction end cell end table end style$

Diperoleh $begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 3 x minus 10 over denominator 2 end fraction end style$ maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis 2 right parenthesis end cell equals cell fraction numerator 3.2 minus 10 over denominator 2 end fraction space end cell row cell g left parenthesis 2 right parenthesis end cell equals cell fraction numerator 6 minus 10 over denominator 2 end fraction space end cell row cell g left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 4 over denominator 2 end fraction space end cell row cell g left parenthesis 2 right parenthesis end cell equals cell negative 2 end cell end table end style$

Dengan demikian, nilai dari adalah .