Tentukan invers fungsi H(x)=35+2x

Pertanyaan

Tentukan invers fungsi $\style{font-size:14px}{H(x)=\sqrt[3]{5+2\sqrt x}}$

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

invers dari fungsi

adalah $begin mathsize 14px style bold italic H to the power of bold minus bold 1 end exponent begin bold style left parenthesis x right parenthesis end style bold equals begin bold style left parenthesis fraction numerator x cubed minus 5 over denominator 2 end fraction right parenthesis end style to the power of bold 2 end style$

Pembahasan

Ingat!

Berdasarkan konsep tersebut diperoleh

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

Sehingga $begin mathsize 14px style H to the power of negative 1 end exponent left parenthesis y right parenthesis equals open parentheses fraction numerator y cubed minus 5 over denominator 2 end fraction close parentheses squared end style$ atau $begin mathsize 14px style H to the power of negative 1 end exponent open parentheses x close parentheses equals open parentheses fraction numerator x cubed minus 5 over denominator 2 end fraction close parentheses squared end style$

Jadi, invers dari fungsi adalah $begin mathsize 14px style bold italic H to the power of bold minus bold 1 end exponent begin bold style left parenthesis x right parenthesis end style bold equals begin bold style left parenthesis fraction numerator x cubed minus 5 over denominator 2 end fraction right parenthesis end style to the power of bold 2 end style$