Tentukan fungsi (f∘g∘h)(x), jika f(x)=3x+6, g(x)=2x2−4, dan h(x)=xx+3, x=0.

Pertanyaan

Tentukan fungsi $\style{font-size:14px}{\left(f\circ g\circ h\right)\left(x\right)}$ , jika $\style{font-size:14px}{f(x)=3x+6}$ , $\style{font-size:14px}{g(x)=2x^2-4}$ , dan $begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator x plus 3 over denominator x end fraction comma space x not equal to 0 end style$ .

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

diperoleh $begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses left parenthesis x right parenthesis equals fraction numerator 36 x plus 54 over denominator x squared end fraction end style$ .

Pembahasan

Diketahui , , dan $begin mathsize 14px style h left parenthesis x right parenthesis equals fraction numerator x plus 3 over denominator x end fraction comma space x not equal to 0 end style$ . Akan dicari .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g ring operator h right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses fraction numerator x plus 3 over denominator x end fraction close parentheses close parentheses end cell row blank equals cell f open parentheses 2 open parentheses fraction numerator x plus 3 over denominator x end fraction close parentheses squared minus 4 close parentheses end cell row blank equals cell f open parentheses 2 open parentheses fraction numerator x squared plus 6 x plus 9 over denominator x squared end fraction close parentheses minus 4 close parentheses end cell row blank equals cell f open parentheses fraction numerator 2 x squared plus 12 x plus 18 minus 4 x squared over denominator x squared end fraction close parentheses end cell row blank equals cell f open parentheses fraction numerator negative 2 x squared plus 12 x plus 18 over denominator x squared end fraction close parentheses end cell row blank equals cell 3 open parentheses fraction numerator negative 2 x squared plus 12 x plus 18 over denominator x squared end fraction close parentheses plus 6 end cell row blank equals cell fraction numerator negative 6 x squared plus 36 x plus 54 over denominator x squared end fraction plus 6 end cell row blank equals cell fraction numerator negative 6 x squared plus 36 x plus 54 plus 6 x squared over denominator x squared end fraction end cell row blank equals cell fraction numerator 36 x plus 54 over denominator x squared end fraction end cell end table end style$

Jadi, diperoleh $begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses left parenthesis x right parenthesis equals fraction numerator 36 x plus 54 over denominator x squared end fraction end style$ .