tolong bantuin jawab dong please
[tex]f(x)=2x+3\\g(x)=-4x-5[/tex]
a)
[tex](f\,o\,g)(x)=f(g(x))\\\\(f\,o\,g)(x)=f(-4x-5)\\\\(f\,o\,g)(x)=2(-4x-5)+3\\\\(f\,o\,g)(x)=(-8x-10)+3\\\\(f\,o\,g)(x)=-8x-7[/tex]
Mencari invers
[tex](f\,o\,g)(x)=-8x-7\\\\y=-8x-7\\\\-8x=y+7\\\\x=\frac{y+7}{-8}\\\\(f\,o\,g)^{-1}(x)=\frac{x+7}{-8}[/tex]
Maka,
[tex](f\,o\,g)^{-1}(-2)=\frac{(-2)+7}{-8}\\\\(f\,o\,g)^{-1}(-2)=\frac{5}{-8}=-\frac{5}{8}[/tex]
b)
[tex](g\,o\,f)(x)=g(f(x))\\\\(g\,o\,f)(x)=g(2x+3)\\\\(g\,o\,f)(x)=-4(2x+3)-5\\\\(g\,o\,f)(x)=(-8x-12)-5\\\\(g\,o\,f)(x)=-8x-17[/tex]
Mencari invers
[tex](g\,o\,f)(x)=-8x-17\\\\y=-8x-17\\\\-8x=y+17\\\\x=\frac{y+17}{-8}\\\\(g\,o\,f)^{-1}(x)=\frac{x+17}{-8}\\\\[/tex]
Maka,
[tex](g\,o\,f)^{-1}(3)=\frac{3+17}{-8}\\\\(g\,o\,f)^{-1}(3)=\frac{20}{-8}=-\frac{5}{2}[/tex]
