Diketahui fungsi f(2x1)=x+4 dan g(x)=x−3x+1, x=3. Rumus komposisi fungsi (g∘f)(x) adalah ....

Pertanyaan

Diketahui fungsi $begin mathsize 14px style f open parentheses fraction numerator 1 over denominator 2 x end fraction close parentheses equals x plus 4 end style$ dan $begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator x minus 3 end fraction end style$ , $\style{font-size:14px}{x\neq3}$ . Rumus komposisi fungsi $\style{font-size:14px}{(g\circ f)(x)}$ adalah ....

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end style$ .

Pembahasan

Diketahui $begin mathsize 14px style f open parentheses fraction numerator 1 over denominator 2 x end fraction close parentheses equals x plus 4 end style$ , misalkan $begin mathsize 14px style y equals fraction numerator 1 over denominator 2 x end fraction end style$ maka diperoleh $begin mathsize 14px style x equals fraction numerator 1 over denominator 2 y end fraction end style$ sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses y close parentheses end cell equals cell fraction numerator 1 over denominator 2 y end fraction plus 4 end cell row blank equals cell fraction numerator 1 plus 8 y over denominator 2 y end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 1 plus 8 x over denominator 2 x end fraction end cell row blank blank blank end table end style$

dengan demikian komposisi fungsi adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses plus 1 over denominator open parentheses fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator fraction numerator 1 plus 8 x plus 2 x over denominator 2 x end fraction over denominator fraction numerator 1 plus 8 x minus 6 x over denominator 2 x end fraction end fraction end cell row blank equals cell fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end style$ .