Fungsi f(x)2x+5/x-7. maka f invers(x-1) adalah.... Question from @novitakh

October 2018 2 20 Report

Fungsi f(x)2x+5/x-7. maka f invers(x-1) adalah

Brillianttt Bila f(x) = ax+b / cx+d
maka f⁻¹(x) = -dx+b /cx-a

f(x) = 2x+5 / x-7
f⁻¹(x) = 7x+5 / x-2
maka
f⁻¹(x-1) = 7(x-1)+5 / x-1-2
= 7x -7+5 / x-3
= 7x-2 / x-3

0 votes Thanks 1

anaoov $f(x) = \frac{2x+5}{x-7} = \frac{ax+b}{cx+d} \\ f ^{-1} (x)= \frac{-dx+b}{cx-a} \\ f ^{-1} (x)= \frac{7x+5}{x-2}$

atau
$f(x) = \frac{2x+5}{x-7} \\ y = \frac{2x+5}{x-7} \\ y(x-7) = 2x+5 \\ xy - 7y = 2x+5 \\ xy - 2x = 7y + 5 \\ x(y-2) = 7y+5 \\ x= \frac{7y+5}{y-2} \\ \\ f ^{-1} (x)= \frac{7x+5}{x-2}$

maka,
$f ^{-1} (x-1)= \frac{7(x-1)+5}{(x-1)-2} \\ f ^{-1} (x-1)= \frac{7x-7+5}{x-3} \\ f ^{-1} (x-1)= \frac{7x-2}{x-3}$

0 votes Thanks 1

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