Roboguru

Diketahui fungsi , , dan  dengan , , dan . Tentukan  jika: b.

Pertanyaan

Diketahui fungsi begin mathsize 14px style f colon space straight real numbers rightwards arrow straight real numbers end styleError converting from MathML to accessible text., dan Error converting from MathML to accessible text. dengan begin mathsize 14px style f open parentheses x close parentheses equals x minus 1 end stylebegin mathsize 14px style g open parentheses x close parentheses equals 5 minus 2 x end style, dan begin mathsize 14px style h open parentheses x close parentheses equals x squared plus 3 x minus 2 end style. Tentukan begin mathsize 14px style x end style jika:

b. begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equals 8 end style 

Pembahasan Soal:

Gunakan konsep komposisi fungsi untuk menentukan nilai dari begin mathsize 14px style x end style.

Diketahui:

begin mathsize 14px style f open parentheses x close parentheses equals x minus 1 end style

begin mathsize 14px style g open parentheses x close parentheses equals 5 minus 2 x end style

begin mathsize 14px style h open parentheses x close parentheses equals x squared plus 3 x minus 2 end style

Akan ditentukan nilai begin mathsize 14px style x end style jika begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equals 8 end style.

Terlebih dahulu tentukan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 5 minus 2 x close parentheses end cell row blank equals cell open parentheses 5 minus 2 x close parentheses minus 1 end cell row blank equals cell 5 minus 2 x minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell negative 2 x plus 4 end cell end table end style 

Akan ditentukan nilai begin mathsize 14px style x end style jika begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equals 8 end style, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end cell equals 8 row cell h open parentheses open parentheses f ring operator g close parentheses open parentheses x close parentheses close parentheses end cell equals 8 row cell h open parentheses negative 2 x plus 4 close parentheses end cell equals 8 row cell open parentheses negative 2 x plus 4 close parentheses squared plus 3 open parentheses negative 2 x plus 4 close parentheses minus 2 end cell equals 8 row cell 4 x squared minus 16 x plus 16 minus 6 x plus 12 minus 2 end cell equals 8 row cell 4 x squared minus 22 x plus 26 end cell equals 8 row cell 4 x squared minus 22 x plus 26 minus 8 end cell equals 0 row cell 4 x squared minus 22 x plus 18 end cell equals 0 row cell 2 x squared minus 11 x plus 9 end cell equals 0 row cell open parentheses 2 x minus 9 close parentheses open parentheses x minus 2 close parentheses end cell equals 0 row cell 2 x minus 9 equals 0 space space space space space atau space x minus 2 equals 0 end cell blank blank row cell 2 x equals 9 space space space space atau space space space space space space space x equals 2 end cell blank blank row cell x equals 9 over 2 space space space space atau space space space space space space space x equals 2 end cell blank blank row cell x equals 4 1 half space space space atau space space space space space space space x equals 2 end cell blank blank end table end style  

Jadi, nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style open curly brackets 2 comma space 4 1 half close curly brackets end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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