Pertanyaan

Diketahui fungsi g ( x ) = 2 x − 4 dan ( f ∘ g ) ( x ) = 5 x − 9 7 x + 3 . Nilai dari f ( 2 ) ....

Diketahui fungsi $g (x) = 2 x - 4$ dan $(f \circ g) (x) = \frac{7 x + 3}{5 x - 9}$ . Nilai dari $f (2)$ ....

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Pembahasan

Dengan menggunakan konsep fungsi komposisi, didapatkan Jadi, nilai dari .

Dengan menggunakan konsep fungsi komposisi, didapatkan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x plus 3 over denominator 5 x minus 9 end fraction end cell row cell f open parentheses 2 x minus 4 close parentheses end cell equals cell fraction numerator 7 x plus 3 over denominator 5 x minus 9 end fraction end cell row blank blank blank row cell 2 x minus 4 end cell equals a row cell 2 x end cell equals cell a plus 4 end cell row x equals cell fraction numerator a plus 4 over denominator 2 end fraction end cell row blank blank blank row cell f left parenthesis a right parenthesis end cell equals cell fraction numerator 7 open parentheses fraction numerator a plus 4 over denominator 2 end fraction close parentheses plus 3 over denominator 5 open parentheses fraction numerator a plus 4 over denominator 2 end fraction close parentheses minus 9 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 a plus 28 over denominator 2 end fraction end style plus 3 over denominator begin display style fraction numerator 5 a plus 20 over denominator 2 end fraction end style minus 9 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 7 a plus 34 over denominator 2 end fraction end style over denominator begin display style fraction numerator 5 a plus 2 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 7 a plus 34 over denominator 5 a plus 2 end fraction end cell row blank blank blank row cell f left parenthesis 2 right parenthesis end cell equals cell fraction numerator 7 left parenthesis 2 right parenthesis plus 34 over denominator 5 left parenthesis 2 right parenthesis plus 2 end fraction end cell row blank equals cell fraction numerator 14 plus 34 over denominator 10 plus 2 end fraction end cell row blank equals cell 48 over 12 end cell row blank equals 4 end table end style$

Jadi, nilai dari .