Roboguru

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

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:

a. begin mathsize 14px style open parentheses f ring operator h ring operator g close parentheses open parentheses x close parentheses equals 15 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 f ring operator h ring operator g close parentheses open parentheses x close parentheses equals 15 end style.

Terlebih dahulu tentukan begin mathsize 14px style open parentheses h 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 h ring operator g close parentheses open parentheses x close parentheses end cell equals cell h open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell h open parentheses 5 minus 2 x close parentheses end cell row blank equals cell open parentheses 5 minus 2 x close parentheses squared plus 3 open parentheses 5 minus 2 x close parentheses minus 2 end cell row blank equals cell 25 minus 20 x plus 4 x squared plus 15 minus 6 x minus 2 end cell row cell open parentheses h ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared minus 26 x plus 38 end cell end table end style  

Akan ditentukan nilai begin mathsize 14px style x end style jika begin mathsize 14px style open parentheses f ring operator h ring operator g close parentheses open parentheses x close parentheses equals 15 end style, diperoleh:

  begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses f ring operator h ring operator g close parentheses open parentheses x close parentheses end cell equals 15 row cell f open parentheses open parentheses h ring operator g close parentheses open parentheses x close parentheses close parentheses end cell equals 15 row cell f open parentheses 4 x squared minus 26 x plus 38 close parentheses end cell equals 15 row cell open parentheses 4 x squared minus 26 x plus 38 close parentheses minus 1 end cell equals 15 row cell 4 x squared minus 26 x plus 37 end cell equals 15 row cell 4 x squared minus 26 x plus 37 minus 15 end cell equals 0 row cell 4 x squared minus 26 x plus 22 end cell equals 0 row cell 2 x squared minus 13 x plus 11 end cell equals 0 row cell open parentheses 2 x minus 11 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 row cell 2 x minus 11 equals 0 space a t a u space x minus 1 equals 0 end cell blank blank row cell 2 x equals 11 space a t a u space space space space space space x equals 1 end cell blank blank row cell x equals 11 over 2 space a t a u space space space space space space x equals 1 end cell blank blank row cell x equals 5 1 half space a t a u space space space space space space x equals 1 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 1 comma space 5 1 half close curly brackets end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 Maret 2021

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