Roboguru

Diketahui:   Tentukan! a) fungsi   b) fungsi komposisi

Pertanyaan

Diketahui:

begin mathsize 14px style open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals 9 x squared plus 12 x plus 1 g left parenthesis x right parenthesis equals x squared minus 3 end style 

Tentukan!

a) fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style 

b) fungsi komposisi begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end style 

Pembahasan Soal:

Fungsi komposisi merupakan suatu penggabungan dari suatu opersasi dua jenis fungsi undefined dan juga begin mathsize 14px style g left parenthesis x right parenthesis end style sehingga mampu menghasilkan fungsi baru.

a) 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row cell 9 x squared plus 12 x plus 1 end cell equals cell left parenthesis f left parenthesis x right parenthesis right parenthesis squared minus 3 end cell row cell 9 x squared plus 12 x plus 4 end cell equals cell left parenthesis f left parenthesis x right parenthesis right parenthesis squared end cell row cell open parentheses 3 x plus 2 close parentheses open parentheses 3 x plus 2 close parentheses end cell equals cell left parenthesis f left parenthesis x right parenthesis right parenthesis squared end cell row cell space left parenthesis 3 x plus 2 right parenthesis to the power of up diagonal strike 2 end exponent end cell equals cell left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of up diagonal strike 2 end exponent end cell row cell space 3 x plus 2 end cell equals cell f left parenthesis x right parenthesis end cell end table end style

Maka, fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x plus 2 end style.

b)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 3 left parenthesis g left parenthesis x right parenthesis right parenthesis plus 2 end cell row blank equals cell 3 left parenthesis x squared minus 3 right parenthesis plus 2 end cell row blank equals cell 3 x squared minus 9 plus 2 end cell row blank equals cell 3 x squared minus 7 end cell end table end style

Maka, fungsi komposisi undefined adalah begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals 3 x squared minus 7 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

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