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Diketahui f ( x ) = 2 x + 3 , g ( x ) = x + 1 1 dan h ( x ) = x 2 − 4 . Tentukan a. ( h ∘ g ∘ f ) ( x )

Diketahui $f (x) = 2 x + 3, g (x) = \frac{1}{x + 1} dan h (x) = x^{2} - 4$ . Tentukan

a. $(h \circ g \circ f) (x)$

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Pembahasan

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis h ring operator g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell h left parenthesis g left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell h left parenthesis g left parenthesis 2 x plus 3 right parenthesis right parenthesis end cell row blank equals cell h open parentheses fraction numerator 1 over denominator left parenthesis 2 x plus 3 right parenthesis plus 1 end fraction close parentheses end cell row blank equals cell equals h open parentheses fraction numerator 1 over denominator 2 x plus 4 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 1 over denominator 2 x plus 4 end fraction close parentheses squared minus 4 end cell row blank equals cell fraction numerator 1 over denominator 4 x squared plus 16 x plus 16 end fraction minus 4 end cell row blank equals cell fraction numerator 1 minus 4 left parenthesis 4 x squared plus 16 x plus 16 right parenthesis over denominator 4 x squared plus 16 x plus 16 end fraction end cell row blank equals cell fraction numerator 1 minus 16 x squared minus 64 x minus 64 over denominator 4 x squared plus 16 x plus 16 end fraction end cell row blank equals cell fraction numerator negative 16 x squared minus 64 x minus 63 over denominator 4 x squared plus 16 x plus 16 end fraction end cell end table$

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