Roboguru

Diketahui   dan . Jika   Tentukan nilai dari !

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 1 over x end style  dan begin mathsize 14px style g left parenthesis x right parenthesis equals x minus 1 end style. Jika begin mathsize 14px style open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals 0 end style 
Tentukan nilai dari begin mathsize 14px style x end style!

  1. ...space 

  2. ...begin mathsize 14px style space end style 

Jawaban:

Ingat: konsep komposisi dua fungsi begin mathsize 14px style f ring operator g open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style 

Diketahui: undefined , undefined dan begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals 0 end style 
Maka

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

begin mathsize 14px style Misal colon space y equals f ring operator g left parenthesis x right parenthesis end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 1 over denominator x minus 1 end fraction end cell row cell x y minus y end cell equals 1 row cell x y end cell equals cell 1 plus y end cell row x equals cell fraction numerator 1 plus y over denominator y end fraction end cell end table end style 

begin mathsize 14px style sehingga colon space open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 1 plus x over denominator x end fraction end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals 0 row cell fraction numerator 1 plus x over denominator x end fraction end cell equals 0 row cell 1 plus x end cell equals 0 row x equals cell negative 1 end cell end table end style   

Jadi, nilai begin mathsize 14px style bold italic x bold equals bold minus bold 1 end style

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