Pertanyaan

Jika f ( x ) = 3 x + 6 , g ( x ) = 2 x 2 − 4 , dan h ( x ) = x x + 3 , x  = 0 , fungsi ( f ∘ g ∘ h ) ( x ) = ...

Jika $f (x) = 3 x + 6, g (x) = 2 x^{2} - 4$ , dan $h (x) = \frac{x + 3}{x}, x \neq = 0$ , fungsi $(f \circ g \circ h) (x) =$ ...

$begin mathsize 14px style fraction numerator 4 x squared plus 12 x plus 18 over denominator x squared end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 4 x squared plus 12 x minus 3 over denominator x squared end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 4 x squared plus 36 x plus 18 over denominator x squared end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 36 x plus 54 over denominator x squared end fraction comma space x not equal to 0 end style$
$begin mathsize 14px style fraction numerator 12 x plus 18 over denominator x squared end fraction comma space x not equal to 0 end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

misalkan maka Jadi, jawaban yang tepat adalah D.

misalkan

maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis h left parenthesis x right parenthesis right parenthesis end cell row blank equals cell g open parentheses fraction numerator x plus 3 over denominator x end fraction close parentheses end cell row blank equals cell 2 open parentheses fraction numerator x plus 3 over denominator x end fraction close parentheses squared minus 4 end cell row blank equals cell 2 open parentheses fraction numerator x squared plus 6 x plus 9 over denominator x squared end fraction close parentheses minus 4 end cell row blank equals cell fraction numerator 2 x squared plus 12 x plus 18 over denominator x squared end fraction minus fraction numerator 4 x squared over denominator x squared end fraction end cell row cell left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator negative 2 x squared plus 12 x plus 18 over denominator x squared end fraction end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator m right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis m open parentheses x close parentheses right parenthesis end cell row blank equals cell f open parentheses fraction numerator negative 2 x squared plus 12 x plus 18 over denominator x squared end fraction close parentheses end cell row blank equals cell 3 open parentheses fraction numerator negative 2 x squared plus 12 x plus 18 over denominator x squared end fraction close parentheses plus 6 end cell row blank equals cell fraction numerator negative 6 x squared plus 36 x plus 54 over denominator x squared end fraction plus fraction numerator 6 x squared over denominator x squared end fraction end cell row cell left parenthesis f ring operator m right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 36 x plus 54 over denominator x squared end fraction end cell row cell open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 36 x plus 54 over denominator x squared end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah D.

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