Roboguru

Diketahui  dan , tentukan  dan

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals 1 half x minus 3 dan g left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x plus 4 end fraction, tentukan left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis dan left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis 

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals 1 half x minus 3 dan g left parenthesis x right parenthesis equals fraction numerator x minus 2 over denominator x plus 4 end fraction

Cari f to the power of negative 1 end exponent left parenthesis x right parenthesis space dan space g to the power of negative 1 end exponent left parenthesis x right parenthesis terlebih dahulu 

Ingat kembali bahwa jika f left parenthesis x right parenthesis equals a x plus b maka f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus b over denominator a end fraction sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 1 half x minus 3 end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus left parenthesis negative 3 right parenthesis over denominator begin display style 1 half end style end fraction end cell row blank equals cell 2 left parenthesis x plus 3 right parenthesis end cell row blank equals cell 2 x plus 6 end cell end table 

Ingat kembali jika f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator x c plus d end fraction maka f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative d x plus b over denominator c x minus a end fraction sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 2 over denominator x plus 4 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator negative 4 x plus left parenthesis negative 2 right parenthesis over denominator x minus 1 end fraction end cell row blank equals cell fraction numerator negative 4 x minus 2 over denominator x minus 1 end fraction end cell end table 

Ingat bahwa left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis  

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row blank equals cell f to the power of negative 1 end exponent left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f to the power of negative 1 end exponent open parentheses fraction numerator negative 4 x minus 2 over denominator x minus 1 end fraction close parentheses end cell row blank equals cell 2 open parentheses fraction numerator negative 4 x minus 2 over denominator x minus 1 end fraction close parentheses plus 6 end cell row blank equals cell fraction numerator negative 8 x minus 4 over denominator x minus 1 end fraction plus fraction numerator 6 x minus 6 over denominator x minus 1 end fraction end cell row blank equals cell fraction numerator negative 2 x minus 10 over denominator x minus 1 end fraction end cell end table   

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g to the power of negative 1 end exponent left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g to the power of negative 1 end exponent left parenthesis 2 x plus 6 right parenthesis end cell row blank equals cell fraction numerator negative 4 left parenthesis 2 x plus 6 right parenthesis minus 2 over denominator left parenthesis 2 x plus 6 right parenthesis minus 1 end fraction end cell row blank equals cell fraction numerator negative 8 x minus 24 minus 2 over denominator 2 x plus 5 end fraction end cell row blank equals cell fraction numerator negative 8 x minus 26 over denominator 2 x plus 5 end fraction end cell end table  

Jadi,  left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis dan left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis berturut-turut adalah fraction numerator negative 2 x minus 10 over denominator x minus 1 end fraction dan fraction numerator negative 8 x minus 26 over denominator 2 x plus 5 end fraction 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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