Pertanyaan

Diketahui fungsi f ( x ) = − x − 8 , g ( x ) = 3 2 x − 5 dan h ( x ) = 3 x + 4 . Jika k ( x ) = ( f − g ) ( x ) , invers dari ( h ∘ k ) ( x ) adalah ...

Diketahui fungsi $f (x) = - x - 8, g (x) = \frac{2 x - 5}{3} dan h (x) = 3 x + 4$ . Jika $k (x) = (f - g) (x)$ , invers dari $(h \circ k) (x)$ adalah $...$

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 15 over denominator 5 end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x plus 5 over denominator 5 end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 15 minus x over denominator 5 end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 5 x plus 19 over denominator 3 end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 5 x minus 19 over denominator 3 end fraction end cell end table$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Menentukan : Menentukan : Menentukan : Oleh karena itu, jawaban yang benar adalah A.

Menentukan k left parenthesis x right parenthesis equals left parenthesis f minus g right parenthesis left parenthesis x right parenthesis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell k left parenthesis x right parenthesis end cell equals cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell row blank equals cell f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis end cell row blank equals cell left parenthesis negative x minus 8 right parenthesis minus open parentheses fraction numerator 2 x minus 5 over denominator 3 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator negative 3 x minus 24 over denominator 3 end fraction close parentheses minus open parentheses fraction numerator 2 x minus 5 over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator negative 5 x minus 19 over denominator 3 end fraction end cell end table$

Menentukan open parentheses h ring operator k close parentheses left parenthesis x right parenthesis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator k close parentheses left parenthesis x right parenthesis end cell equals cell h left parenthesis k left parenthesis x right parenthesis right parenthesis end cell row blank equals cell h open parentheses fraction numerator negative 5 x minus 19 over denominator 3 end fraction close parentheses end cell row blank equals cell 3 open parentheses fraction numerator negative 5 x minus 19 over denominator 3 end fraction close parentheses plus 4 end cell row blank equals cell negative 5 x minus 19 plus 4 end cell row blank equals cell negative 5 x minus 15 end cell end table$

Menentukan open parentheses h ring operator k close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis :

$table attributes columnalign right center left columnspacing 0px end attributes row cell Misalnya colon space open parentheses h ring operator k close parentheses left parenthesis x right parenthesis end cell equals cell y space rightwards arrow open parentheses h ring operator k close parentheses to the power of negative 1 end exponent left parenthesis y right parenthesis equals x end cell row blank blank blank row y equals cell negative 5 x minus 15 end cell row cell 5 x end cell equals cell negative y minus 15 end cell row x equals cell fraction numerator negative y minus 15 over denominator 5 end fraction end cell row x equals cell negative fraction numerator y plus 15 over denominator 5 end fraction end cell row cell open parentheses h ring operator k close parentheses to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell negative fraction numerator y plus 15 over denominator 5 end fraction end cell row cell open parentheses h ring operator k close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell negative fraction numerator x plus 15 over denominator 5 end fraction end cell end table$

Oleh karena itu, jawaban yang benar adalah A.

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