Pertanyaan

Diketahui f ( x ) = 2 x x − 6 , x  = 0 dan g ( x ) = 2 x − 7 . Tentukan ( g ∘ f ) − 1 ( x )

Diketahui $f (x) = \frac{x - 6}{2 x}, x \neq = 0$ dan $g (x) = 2 x - 7$ . Tentukan $(g \circ f)^{- 1} (x)$

$begin mathsize 14px style space left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses equals negative fraction numerator 6 over denominator x plus 6 end fraction comma x not equal to negative 6 end style$
$begin mathsize 14px style space left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 over denominator x plus 6 end fraction comma x not equal to negative 6 end style$
$begin mathsize 14px style space left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 over denominator x minus 6 end fraction comma x not equal to 6 end style$
$begin mathsize 14px style space left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 1 over denominator x minus 6 end fraction comma x not equal to 6 end style$
$begin mathsize 14px style space left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses equals negative fraction numerator 1 over denominator x plus 6 end fraction comma x not equal to negative 6 end style$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

Jawaban yang tepat adalah A

Pembahasan

Pertama kita menntukan fungsi komposisi Sehingga, Jadi, Jawaban yang tepat adalah A

Pertama kita menntukan fungsi komposisi begin mathsize 14px style space left parenthesis g ring operator f right parenthesis open parentheses x close parentheses end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space left parenthesis g ring operator f right parenthesis open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses fraction numerator x minus 6 over denominator 2 x end fraction close parentheses end cell row blank equals cell 2 open parentheses fraction numerator x minus 6 over denominator 2 x end fraction close parentheses minus 7 end cell row blank equals cell fraction numerator x minus 6 over denominator x end fraction minus 7 end cell row blank equals cell fraction numerator x minus 6 over denominator x end fraction minus fraction numerator 7 x over denominator x end fraction end cell row blank equals cell fraction numerator x minus 6 minus 7 x over denominator x end fraction end cell row blank equals cell fraction numerator negative 6 x minus 6 over denominator x end fraction end cell end table end style$

Sehingga,

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Jadi, Jawaban yang tepat adalah A