Pertanyaan

Diketahui fungsi f ( x ) = 4 x + 1 dan g ( x ) = 4 x − 3 x + 5 , x  = 4 3 . Invers fungsi ( f ∘ g ) ( x ) adalah ...

Diketahui fungsi $f (x) = 4 x + 1$ dan $g (x) = \frac{x + 5}{4 x - 3}, x \neq = \frac{3}{4}$ . Invers fungsi $(f \circ g) (x)$ adalah ...

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

invers fungsi adalah .

invers fungsi open parentheses f ring operator g close parentheses left parenthesis x right parenthesis

adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses f ring operator g close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x plus 17 over denominator 4 x minus 8 end fraction end cell end table$ .

Pembahasan

Diketahui: Komposisi dua fungsi : Invers fungsi dengan mengubah ke variabel telebih dahulu. Maka inversnya adalah: Jadi, invers fungsi adalah .

Diketahui:

f left parenthesis x right parenthesis equals 4 x plus 1
$g left parenthesis x right parenthesis equals fraction numerator x plus 5 over denominator 4 x minus 3 end fraction comma space x not equal to 3 over 4$

Komposisi dua fungsi open parentheses f ring operator g close parentheses left parenthesis x right parenthesis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell 4 open parentheses fraction numerator x plus 5 over denominator 4 x minus 3 end fraction close parentheses plus 1 end cell row blank equals cell fraction numerator 4 x plus 20 over denominator 4 x minus 3 end fraction plus 1 end cell row blank equals cell fraction numerator 4 x plus 20 plus 4 x minus 3 over denominator 4 x minus 3 end fraction end cell row blank equals cell fraction numerator 8 x plus 17 over denominator 4 x minus 3 end fraction end cell end table$

Invers fungsi open parentheses f ring operator g close parentheses left parenthesis x right parenthesis dengan mengubah ke variabel telebih dahulu.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell fraction numerator 8 x plus 17 over denominator 4 x minus 3 end fraction end cell row y equals cell fraction numerator 8 x plus 17 over denominator 4 x minus 3 end fraction end cell row cell 4 x y minus 3 y end cell equals cell 8 x plus 17 end cell row cell 4 x y minus 8 x end cell equals cell 3 y plus 17 end cell row cell x open parentheses 4 y minus 8 close parentheses end cell equals cell 3 y plus 17 end cell row x equals cell fraction numerator 3 y plus 17 over denominator 4 y minus 8 end fraction end cell end table$

Maka inversnya adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator 3 y plus 17 over denominator 4 y minus 8 end fraction end cell row cell y apostrophe end cell equals cell fraction numerator 3 x plus 17 over denominator 4 x minus 8 end fraction end cell row cell open parentheses f ring operator g close parentheses apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 3 x plus 17 over denominator 4 x minus 8 end fraction end cell end table$

Jadi, invers fungsi open parentheses f ring operator g close parentheses left parenthesis x right parenthesis adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses f ring operator g close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x plus 17 over denominator 4 x minus 8 end fraction end cell end table$ .

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