Pertanyaan

Diketahui: f ( x ) = 5 x + 3 g ( x ) = x 1 Ditanya ( f − 1 ∘ g − 1 ) ( x ) adalah ....

Diketahui:

$f (x) = 5 x + 3 g (x) = \frac{1}{x}$

Ditanya $(f^{- 1} \circ g^{- 1}) (x)$ adalah ....

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Habis dalam

Klaim

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

.

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

Pembahasan

Ingat bahwa . Pertama, cari terlebih dahulu . Lalu kita cari nilai invers dari dengan cara memisalkan sebagai . Jadi .

Ingat bahwa open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis equals open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis . Pertama, cari terlebih dahulu .

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

Lalu kita cari nilai invers dari open parentheses g ring operator f close parentheses left parenthesis x right parenthesis dengan cara memisalkan sebagai .

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 1 over denominator 5 x plus 3 end fraction end cell row cell left parenthesis 5 x plus 3 right parenthesis times y end cell equals 1 row cell 5 x y plus 3 y end cell equals 1 row cell 5 x y end cell equals cell 1 minus 3 y end cell row x equals cell fraction numerator 1 minus 3 y over denominator 5 y end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 1 minus 3 x over denominator 5 x end fraction end cell end table$

Jadi $table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis end cell equals cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus 3 x over denominator 5 x end fraction end cell end table$ .