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Fungsi begin mathsize 14px style f colon R rightwards arrow R comma space g colon R rightwards arrow R comma space dan space h colon R rightwards arrow R end style ditentukan oleh begin mathsize 14px style f left parenthesis x right parenthesis equals x minus 3 comma space left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals x squared end style dan begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction space end styledengan size 14px x size 14px not equal to size 14px 3. Tentukan:

a. begin mathsize 14px style g left parenthesis x right parenthesis space dan space h to the power of negative 1 end exponent left parenthesis x right parenthesis end style

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Pembahasan

fungsi g(x) dapat ditentukan sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell x squared end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell x squared end cell row cell g left parenthesis x right parenthesis minus 3 end cell equals cell x squared end cell row cell g left parenthesis x right parenthesis end cell equals cell x squared plus 3 end cell end table end style

Untuk invers fungsi h(x), begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction rightwards arrow h 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 end style

sehingga diperoleh:

begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction rightwards arrow h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x plus 1 over denominator x minus 2 end fraction end style

 

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