Diketahui f(x)=x+1; g(x)=2x+1; dan h(x)=3x+1. Nilai (f−1∘g−1∘h−1)(1)=....

Pertanyaan

Diketahui ; ; dan . Nilai ....

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Pembahasan

Diketahui ; ; dan .

menggunakan sifat invers fungsi komposisi:

begin mathsize 14px style open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis equals left parenthesis h ring operator g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end style

kita cari dulu fungsi komposisinya:

begin mathsize 14px style open parentheses h ring operator g ring operator f close parentheses left parenthesis x right parenthesis equals h left parenthesis left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis right parenthesis end style     

                      size 14px equals size 14px h size 14px left parenthesis size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px plus size 14px 1 size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px left parenthesis size 14px x size 14px plus size 14px 1 size 14px right parenthesis size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 2 size 14px plus size 14px 1 size 14px right parenthesis size 14px equals size 14px h size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 3 size 14px right parenthesis size 14px equals size 14px 3 size 14px left parenthesis size 14px 2 size 14px x size 14px plus size 14px 3 size 14px right parenthesis size 14px plus size 14px 1 size 14px equals size 14px 6 size 14px x size 14px plus size 14px 9 size 14px plus size 14px 1 size 14px equals size 14px 6 size 14px x size 14px plus size 14px 10

Selanjutnya kita cari inversnya:

begin mathsize 14px style y equals 6 x plus 10 fraction numerator y minus 10 over denominator 6 end fraction equals x end style

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 10 over denominator 6 end fraction end cell row blank equals cell fraction numerator 1 minus 10 over denominator 6 end fraction end cell row blank equals cell fraction numerator negative 9 over denominator 6 end fraction end cell row blank equals cell negative 1 comma 5 end cell end table

Sehingga Nilai size 14px left parenthesis size 14px f to the power of size 14px minus size 14px 1 end exponent size 14px ring operator size 14px g to the power of size 14px minus size 14px 1 end exponent size 14px ring operator size 14px h to the power of size 14px minus size 14px 1 end exponent size 14px right parenthesis size 14px left parenthesis size 14px 1 size 14px right parenthesis size 14px equals size 14px minus size 14px 1 size 14px comma size 14px 5

Oleh karena itu, jawaban yang benar adalah C.

101

5.0 (4 rating)

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