Ada yang bisa tidak 1 soal saja kalau tidak bisa semuanya, pliss bantu

By Admin ReiPosted on December 5, 2022

Ada yang bisa tidak 1 soal saja kalau tidak bisa semuanya, pliss bantu

Ada yang bisa tidak 1 soal saja kalau tidak bisa semuanya, pliss bantu

$green{huge{1.}}$

$sf f(x)~=~frac{1}{x}$

$sf (f~o~g)(x)~=~frac{x~-~3}{2~-~x}$

$sf fleft(g(x)right)~=~frac{x~-~3}{2~-~x}$

$sf frac{1}{g(x)}~=~frac{x~-~3}{2~-~x}$

$color{darkred}sf g(x)~=~frac{2~-~x}{x~-~3}$

$to~sf y~=~frac{2~-~x}{x~-~3}$

$sf y.(x~-~3)~=~2~-~x$

$sf xy~-~3y~=~2~-~x$

$sf xy~+~x~=~3y~+~2$

$sf x.(y~+~1)~=~3y~+~2$

$sf x~=~frac{3y~+~2}{y~+~1}$

$to~boxed{boxed{pink{sf g^{-1}(x)~=~frac{3x~+~2}{x~+~1}}}}$

$\text{[math]}$

$green{huge{2.}}$

$sf f(x)~=~2x~-~3$

$sf g(x)~=~frac{1}{3x~+~1}$

$sf (f~o~g)(x)~=~2.left(frac{1}{3x~+~1}right)~-~3$

$sf (f~o~g)(x)~=~frac{2}{3x~+~1}~-~3$

$sf (f~o~g)(x)~=~frac{2~-~3.(3x~+~1)}{3x~+~1}$

$sf (f~o~g)(x)~=~frac{2~-~9x~-~3}{3x~+~1}$

$color{darkred}sf (f~o~g)(x)~=~frac{-9x~-~1}{3x~+~1}$

$to~sf y~=~frac{-9x~-~1}{3x~+~1}$

$sf y.(3x~+~1)~=~-9x~-~1$

$sf 3xy~+~y~=~-9x~-~1$

$sf 3xy~+~9x~=~-y~-~1$

$sf x.(3y~+~9)~=~-y~-~1$

$sf x~=~frac{-y~-~1}{3y~+~9}$

$to~boxed{boxed{pink{sf (f~o~g)^{-1}(x)~=~frac{-x~-~1}{3x~+~9}}}}$

$\text{[math]}$

$green{huge{3.}}$

$sf f(x)~=~frac{x~-~1}{x}$

$sf g(x)~=~x~+~3$

$sf (g~o~f)(x)~=~left(frac{x~-~1}{x}right)~+~3$

$sf (g~o~f)(x)~=~frac{(x~-~1)~+~3.(x)}{x}$

$color{darkred}sf (g~o~f)(x)~=~frac{4x~-~1}{x}$

$to~sf y~=~frac{4x~-~1}{x}$

$sf y.(x)~=~4x~-~1$

$sf xy~-~4x~=~-1$

$sf x.(y~-~4)~=~-1$

$sf x.(4~-~y)~=~1$

$sf x~=~frac{1}{4~-~y}$

$to~boxed{boxed{pink{sf (g~o~f)^{-1}(x)~=~frac{1}{4~-~x}}}}$

$\text{[math]}$

$green{huge{4.}}$

$sf h(x)~=~frac{x~-~2}{3}$

$to~sf y~=~frac{x~-~2}{3}$

$sf y.(3)~=~x~-~2$

$sf x~=~3y~+~2to~color{darkred}h^{-1}(x)~=~3x~+~2$

$sf g(x)~=~x~+~7$

$to~sf z~=~x~+~7$

$sf x~=~z~-~7to~color{darkred}g^{-1}(x)~=~x~-~7$

Maka :

$sf left(g^{-1}~o~h^{-1}right)(x)~=~(3x~+~2)~-~7$

$color{darkred}sf left(g^{-1}~o~h^{-1}right)(x)~=~3x~-~5$

Sehingga :

$sf left(g^{-1}~o~h^{-1}right)(it{a}sf )~=~1$

$sf 3.(it{a}sf )~-~5~=~1$

$sf 3it{a}sf ~=~1~+~5$

$sf 3it{a}sf ~=~6to~boxed{boxed{pink{it{a}sf ~=~2}}}$

$\text{[math]}$

$green{huge{5.}}$

$sf f(x)~=~2x~-~20$

$sf g(x)~=~frac{3~-~x}{2}$

$sf (f~o~g)(x)~=~2.left(frac{3~-~x}{2}right)~-~20$

$sf (f~o~g)(x)~=~3~-~x~-~20$

$color{darkred}sf (f~o~g)(x)~=~-x~-~17$

$to~sf y~=~-x~~-~17$

$sf x~=~-y~-~17to~color{darkred}(f~o~g)^{-1}(x)~=~-x~-~17$

Maka :

$sf (f~o~g)^{-1}(4)~=~-4~-~17$

$boxed{boxed{pink{sf (f~o~g)^{-1}(4)~=~-21}}}$

$\text{[math]}$

$green{huge{6.}}$

$sf f(x)~=~frac{x~-~1}{5}$

$to~sf y~=~frac{x~-~1}{5}$

$sf y.(5)~=~x~-~1$

$sf x~=~5y~+~1to~color{darkred}f^{-1}(x)~=~5x~+~1$

$sf g^{-1}(x)~=~frac{3~-~x}{2}$

$to~sf z~=~frac{3~-~x}{2}$

$sf z.(2)~=~3~-~x$

$sf x~=~3~-~2zto~color{darkred}g(x)~=~3~-~2x$

$sf left(f^{-1}~o~gright)(x)~=~5.(3~-~2x)~+~1$

$sf left(f^{-1}~o~gright)(x)~=~15~-~10x~+~1$

$to~color{darkred}sf left(f^{-1}~o~gright)(x)~=~16~-~10x$

$to~sf a~=~16~-~10x$

$sf 10x~=~16~-~a$

$sf x~=~frac{16~-~a}{10}to~color{darkred}left(f^{-1}~o~gright)^{-1}(x)~=~frac{16~-~x}{10}$

Maka :

$sf left(f^{-1}~o~gright)^{-1}(2)~=~frac{16~-~2}{10}~=~frac{14}{10}$

$boxed{boxed{pink{sf left(f^{-1}~o~gright)^{-1}(2)~=~frac{7}{5}}}}$