Pertanyaan

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

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

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nilai adalah

nilai

adalah

Pembahasan

Ingat! Berdasarkan konsep tersebut diperoleh Misalkan , sehingga Maka Jadi, nilai adalah

Ingat!

Berdasarkan konsep tersebut diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator g ring operator f close parentheses open parentheses x close parentheses end cell equals cell h open parentheses g open parentheses f open parentheses x close parentheses close parentheses close parentheses end cell row cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell equals cell h open parentheses g open parentheses 2 x plus 3 close parentheses close parentheses end cell row cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell equals cell h open parentheses 3 open parentheses 2 x plus 3 close parentheses minus 1 close parentheses end cell row cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell equals cell h open parentheses 6 x plus 9 minus 1 close parentheses end cell row cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell equals cell h open parentheses 6 x plus 8 close parentheses end cell end table end style$

Misalkan , sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 x plus 8 end cell equals cell negative 1 end cell row cell 6 x end cell equals cell negative 9 end cell row x equals cell negative 9 over 6 end cell row x equals cell negative 3 over 2 end cell end table end style

Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses 6 x plus 8 close parentheses end cell equals cell fraction numerator x squared minus 1 over denominator x plus 4 end fraction end cell row cell h open parentheses negative 1 close parentheses end cell equals cell fraction numerator open parentheses negative begin display style 3 over 2 end style close parentheses squared minus 1 over denominator open parentheses negative begin display style 3 over 2 end style close parentheses plus 4 end fraction end cell row blank equals cell fraction numerator begin display style 9 over 4 end style minus 1 over denominator begin display style 5 over 2 end style end fraction end cell row blank equals cell fraction numerator begin display style 5 over 4 end style over denominator begin display style 5 over 2 end style end fraction end cell row blank equals cell 1 half end cell end table end style$

Jadi, nilai adalah