Pertanyaan

Diketahui g ( x ) = x + 3 2 x ; x  = − 3 dan h ( x + 1 ) = 3 x − 1 . Nilai ( g ∘ h − 1 ) ( 4 ) ....

Diketahui $g (x) = \frac{2 x}{x + 3}; x \neq = - 3$ dan $h (x + 1) = 3 x - 1$ . Nilai $(g \circ h^{- 1}) (4)$ ....

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nilai dari .

nilai dari left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis equals 16 over 17

left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis equals 16 over 17

Pembahasan

Diketahui Misalkan maka Sehingga, Menentukan invers dari Menentukan Menentukan Jadi, nilai dari .

Diketahui h left parenthesis x plus 1 right parenthesis equals 3 x minus 1

Misalkan a equals x plus 1 maka a minus 1 equals x

Sehingga,

h left parenthesis a right parenthesis equals 3 left parenthesis a minus 1 right parenthesis minus 1 h left parenthesis a right parenthesis equals 3 a minus 3 minus 1 h left parenthesis a right parenthesis equals 3 a minus 4 h left parenthesis x right parenthesis equals 3 x minus 4

Menentukan invers dari h left parenthesis x right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell 3 x minus 4 end cell row y equals cell 3 x minus 4 end cell row cell y plus 4 end cell equals cell 3 x end cell row cell fraction numerator y plus 4 over denominator 3 end fraction end cell equals x row cell fraction numerator y plus 4 over denominator 3 end fraction end cell equals cell h to the power of negative 1 end exponent left parenthesis y right parenthesis end cell row cell fraction numerator x plus 4 over denominator 3 end fraction end cell equals cell h to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table$

Menentukan left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis h to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g open parentheses fraction numerator x plus 4 over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator 2 open parentheses begin display style fraction numerator x plus 4 over denominator 3 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator x plus 4 over denominator 3 end fraction end style close parentheses plus 3 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 x plus 8 over denominator 3 end fraction end style over denominator begin display style fraction numerator x plus 4 plus 9 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 x plus 8 over denominator 3 end fraction times fraction numerator 3 over denominator x plus 13 end fraction end cell row blank equals cell fraction numerator 2 x plus 8 over denominator x plus 13 end fraction end cell end table$

Menentukan left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis end cell equals cell fraction numerator 2 left parenthesis 4 right parenthesis plus 8 over denominator 4 plus 13 end fraction end cell row blank equals cell fraction numerator 8 plus 8 over denominator 17 end fraction end cell row blank equals cell 16 over 17 end cell end table$

Jadi, nilai dari left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis 4 right parenthesis equals 16 over 17 .

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