Diketahui fungsi f(x)=2x−5, g−1(x)=4x+3 dan h−1(x)=8x+1 Nilai (f∘(g∘h))−1(−7) adalah ...

Pertanyaan

Diketahui fungsi $begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 5 comma space g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 3 over denominator 4 end fraction end style$ dan $\style{font-size:14px}{h^{-1}(x)=8x+1}$ Nilai $\style{font-size:14px}{{(f\circ\left(g\circ h\right))}^{-1}\left(-7\right)}$ adalah ...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai fungsi begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style

begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style

adalah 5

Pembahasan

Pertama akan dicari invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 5 end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x minus 5 end cell row cell 2 x end cell equals cell y plus 5 end cell row x equals cell fraction numerator y plus 5 over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 5 over denominator 2 end fraction end cell end table end style$

Dengan menggunakan sifat invers akan ditentukan begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses x close parentheses end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell h to the power of negative 1 end exponent open parentheses open parentheses g to the power of negative 1 end exponent open parentheses open parentheses f to the power of equals 1 end exponent open parentheses x close parentheses close parentheses close parentheses close parentheses close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses fraction numerator x plus 5 over denominator 2 end fraction close parentheses close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell h to the power of negative 1 end exponent open parentheses fraction numerator fraction numerator x plus 5 over denominator 2 end fraction plus 3 over denominator 4 end fraction close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator begin display style fraction numerator x plus 5 plus 6 over denominator 2 end fraction end style over denominator 4 end fraction close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator x plus 11 over denominator 8 end fraction close parentheses end cell row blank equals cell 8 open parentheses fraction numerator x plus 11 over denominator 8 end fraction close parentheses plus 1 end cell row blank equals cell x plus 11 plus 1 end cell row blank equals cell x plus 12 end cell end table end style$

Nilai fugsi adalah begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style

Jadi,nilai fungsi begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style adalah 5