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Jika f(x)=x+52x+3​;x=−5 dan g(x)=3x+1. Tentukanlah f−1(g(x−31​)).

Pertanyaan

Jika f open parentheses x close parentheses equals fraction numerator 2 x plus 3 over denominator x plus 5 end fraction semicolon x not equal to negative 5 dan g open parentheses x close parentheses equals 3 x plus 1. Tentukanlah f to the power of negative 1 end exponent open parentheses g open parentheses x minus 1 third close parentheses close parentheses. 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

bentuk dari bold italic f to the power of bold minus bold 1 end exponent bold left parenthesis bold italic g bold left parenthesis bold x bold minus bevelled bold 1 over bold 3 bold right parenthesis bold right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator bold 3 bold minus bold 15 bold italic x over denominator bold 3 bold italic x bold minus bold 2 end fraction end cell end table.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator bold 3 bold minus bold 15 bold italic x over denominator bold 3 bold italic x bold minus bold 2 end fraction end cell end table.

Ingat sifat berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses x close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses x close parentheses close parentheses end cell end table 

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 3 over denominator x plus 5 end fraction end cell row cell g open parentheses x close parentheses end cell equals cell 3 x plus 1 end cell end table

 Ditanya: f to the power of negative 1 end exponent open parentheses g open parentheses x minus 1 third close parentheses close parentheses.  

Jawab:

Cari f to the power of negative 1 end exponent open parentheses x close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 3 over denominator x plus 5 end fraction end cell row y equals cell fraction numerator 2 x plus 3 over denominator x plus 5 end fraction end cell row cell y open parentheses x plus 5 close parentheses end cell equals cell 2 x plus 3 end cell row cell x y plus 5 y end cell equals cell 2 x plus 3 end cell row cell x y minus 2 x end cell equals cell 3 minus 5 y end cell row cell x open parentheses y minus 2 close parentheses end cell equals cell 3 minus 5 y end cell row x equals cell fraction numerator 3 minus 5 y over denominator y minus 2 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 3 minus 5 y over denominator y minus 2 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 3 minus 5 x over denominator x minus 2 end fraction end cell end table

Cari g open parentheses x minus 1 third close parentheses colon

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell 3 x plus 1 end cell row cell g open parentheses x minus 1 third close parentheses end cell equals cell 3 open parentheses x minus 1 third close parentheses plus 1 end cell row blank equals cell 3 x minus 3 over 3 plus 1 end cell row blank equals cell 3 x end cell row blank equals cell 3 x end cell end table

Cari f to the power of negative 1 end exponent open parentheses g open parentheses x minus 1 third close parentheses close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses g open parentheses x minus 1 third close parentheses close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses 3 x close parentheses end cell row blank equals cell fraction numerator 3 minus 5 open parentheses 3 x close parentheses over denominator open parentheses 3 x close parentheses minus 2 end fraction end cell row blank equals cell fraction numerator 3 minus 15 x over denominator 3 x minus 2 end fraction end cell end table

Dengan demikian, bentuk dari bold italic f to the power of bold minus bold 1 end exponent bold left parenthesis bold italic g bold left parenthesis bold x bold minus bevelled bold 1 over bold 3 bold right parenthesis bold right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator bold 3 bold minus bold 15 bold italic x over denominator bold 3 bold italic x bold minus bold 2 end fraction end cell end table.

68

4.7 (9 rating)

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