Pertanyaan

Tentukan rumus fungsi invers tiap fungsi berikut. b. f ( x ) = x + 3 4 x − 2 , x  = − 3

Tentukan rumus fungsi invers tiap fungsi berikut.

b. $f (x) = \frac{4 x - 2}{x + 3}, x \neq = - 3$

F. Fakhri

Master Teacher

Jawaban terverifikasi

Jawaban

rumus fungsi invers adalah .

rumus fungsi invers

adalah $begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x plus 2 over denominator 4 minus x end fraction comma space x not equal to 4 end style$ .

Pembahasan

Diketahui fungsi . Misalkan , maka: Jadi, rumus fungsi invers adalah .

Diketahui fungsi $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 4 x minus 2 over denominator x plus 3 end fraction comma space x not equal to negative 3 end style$ .

Misalkan , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator 4 x minus 2 over denominator x plus 3 end fraction end cell equals y row cell 4 x minus 2 end cell equals cell y open parentheses x plus 3 close parentheses end cell row cell 4 x minus 2 end cell equals cell y x plus 3 y end cell row cell negative 3 y minus 2 end cell equals cell y x minus 4 x end cell row cell negative 3 y minus 2 end cell equals cell x open parentheses y minus 4 close parentheses end cell row x equals cell fraction numerator negative 3 y minus 2 over denominator y minus 4 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator 3 y plus 2 over denominator 4 minus y end fraction semicolon space y not equal to 4 end cell end table end style$

Jadi, rumus fungsi invers adalah $begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 x plus 2 over denominator 4 minus x end fraction comma space x not equal to 4 end style$ .