Pertanyaan

Diketahui fungsi f : R → R dan g : R → R . Jika diketahui f ( 3 x − 4 ) = 5 x − 1 dan g ( x + 2 ) = x 2 + 3 x − 2 . Nilai Fungsi ( f ∘ g ) ( − 2 ) adalah ...

Diketahui fungsi $f : R \to R$ dan $g : R \to R$ . Jika diketahui $f (3 x - 4) = 5 x - 1$ dan $g (x + 2) = x^{2} + 3 x - 2$ . Nilai Fungsi $(f \circ g) (- 2)$ adalah ...

S. Nur

Master Teacher

Jawaban terverifikasi

Pembahasan

Pertama akan dicari fungsi dengan cara berikut. misal Akan dicari dengan cara berikut misal Selanjutnya akan ditentukan Nilai Fungsi Jadi, nilai dari adalah 9

Pertama akan dicari fungsi begin mathsize 14px style f open parentheses x close parentheses end style dengan cara berikut.

begin mathsize 14px style f open parentheses 3 x minus 4 close parentheses equals 5 x minus 1 end style

misal $begin mathsize 14px style a equals 3 x minus 4 left right double arrow x equals fraction numerator a plus 4 over denominator 3 end fraction end style$

$begin mathsize 14px style f open parentheses a close parentheses equals 5 open parentheses fraction numerator a plus 4 over denominator 3 end fraction close parentheses minus 1 f open parentheses a close parentheses equals fraction numerator 5 a plus 20 minus 3 over denominator 3 end fraction f open parentheses a close parentheses equals fraction numerator 5 a plus 17 over denominator 3 end fraction f open parentheses x close parentheses equals fraction numerator 5 x plus 17 over denominator 3 end fraction end style$

Akan dicari begin mathsize 14px style g open parentheses x close parentheses end style dengan cara berikut

begin mathsize 14px style g open parentheses x plus 2 close parentheses equals x squared plus 3 x minus 2 end style

misal begin mathsize 14px style x plus 2 equals a left right double arrow x equals a minus 2 end style

Selanjutnya akan ditentukan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style

$begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses space space space space space space space space space space space space space equals f open parentheses x squared minus x minus 4 close parentheses space space space space space space space space space space space space space equals fraction numerator 5 open parentheses x squared minus x minus 4 close parentheses plus 17 over denominator 3 end fraction space space space space space space space space space space space space space equals fraction numerator 5 x squared minus 5 x minus 20 plus 17 over denominator 3 end fraction space space space space space space space space space space space space space equals fraction numerator 5 x squared minus 5 x minus 3 over denominator 3 end fraction end style$

Nilai Fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses end style

$begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses equals fraction numerator 5 open parentheses negative 2 close parentheses squared minus 5 open parentheses negative 2 close parentheses minus 3 over denominator 3 end fraction space space space space space space space space space space space space space space space space equals fraction numerator 20 plus 10 minus 3 over denominator 3 end fraction space space space space space space space space space space space space space space space space equals 9 space space space space space end style$

Jadi, nilai dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses end style adalah 9