Roboguru

Tentukan jika .

Tentukan begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style jika begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 2 end style.

Jawaban:

Fungsi invers atau fungsi kebalikan merupakan suatu fungsi yang berkebalikan dari fungsi asalnya.

Jika fungsi asal begin mathsize 14px style f open parentheses x close parentheses equals a x plus b semicolon space a not equal to 0 end style, maka fungsi invers begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus b over denominator a end fraction semicolon space a not equal to 0 end style

Diketahui:

Fungsi begin mathsize 14px style f open parentheses x close parentheses equals 3 x plus 2 end style.

  • Ubahlah bentuk begin mathsize 14px style y equals f open parentheses x close parentheses end style menjadi bentuk begin mathsize 14px style x equals f open parentheses y close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 x plus 2 end cell row y equals cell 3 x plus 2 end cell row cell 3 x end cell equals cell y minus 2 end cell row x equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell end table end style

  • Tuliskan begin mathsize 14px style x end style sebagai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses y close parentheses end style sehingga begin mathsize 14px style f to the power of negative 1 end exponent open parentheses y close parentheses equals f open parentheses y close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell end table end style

  • Ubahlah variabel begin mathsize 14px style y end style dengan begin mathsize 14px style x end style sehingga diperoleh rumus fungsi invers begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y minus 2 over denominator 3 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator 3 end fraction end cell end table end style

Maka, diperoleh begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 2 over denominator 3 end fraction end style.

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