Roboguru

Diketahui:  dan , dengan  dan . Fungsi komposisi  adalah ....

Pertanyaan

Diketahui:

begin mathsize 14px style f left parenthesis x right parenthesis equals x squared plus 4 x end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals negative 2 plus square root of x plus 4 end root end style, dengan begin mathsize 14px style x greater or equal than negative 4 end style dan begin mathsize 14px style x element of straight real numbers end style. Fungsi komposisi begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses end style adalah ....space 

Pembahasan Soal:

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 x squared plus 4 x close parentheses end cell row blank equals cell negative 2 plus square root of open parentheses x squared plus 4 x close parentheses plus 4 end root end cell row blank equals cell negative 2 plus square root of x squared plus 4 x plus 4 end root end cell end table end style

Terdapat dua kemungkinan hasil dari fungsi komposisi diatas, yaitu

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 negative 2 plus square root of x squared plus 4 x plus 4 end root end cell row blank equals cell negative 2 plus square root of open parentheses x plus 2 close parentheses squared end root end cell row blank equals cell negative 2 plus x plus 2 end cell row blank equals x end table end style

atau

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 negative 2 plus square root of x squared plus 4 x plus 4 end root end cell row blank equals cell negative 2 plus square root of open parentheses negative x minus 2 close parentheses squared end root end cell row blank equals cell negative 2 plus left parenthesis negative x minus 2 right parenthesis end cell row blank equals cell negative x minus 4 end cell end table end style

Jadi, fungsi komposisi begin mathsize 14px style bold left parenthesis bold italic g bold ring operator bold italic f bold right parenthesis bold left parenthesis bold italic x bold right parenthesis end style adalah begin mathsize 14px style bold left parenthesis bold italic g bold ring operator bold italic f bold right parenthesis bold left parenthesis bold italic x bold right parenthesis bold equals bold italic x end style atau begin mathsize 14px style bold left parenthesis bold italic g bold ring operator bold italic f bold right parenthesis bold left parenthesis bold italic x bold right parenthesis bold equals bold minus bold italic x bold minus bold 4 end style.undefined 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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