Roboguru

Diketahui  jika  adalah invers dari , maka

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals negative fraction numerator 2 minus 3 x over denominator 2 end fraction end style jika begin mathsize 14px style f to the power of negative 1 end exponent end style adalah invers dari begin mathsize 14px style f end style, maka begin mathsize 14px style f to the power of negative 1 end exponent equals.... end style 

Pembahasan Soal:

Misalkan begin mathsize 14px style y equals f left parenthesis x right parenthesis end style, maka didapat

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

Jadi, invers dari begin mathsize 14px style bold italic f end style adalah begin mathsize 14px style bold italic f to the power of bold minus bold 1 end exponent bold equals fraction numerator bold 2 bold x bold plus bold 2 over denominator bold 3 end fraction end styleundefined 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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