mohon bantuan nya yaaa guyss
[tex]f(x)=x-5\\g(x)=2x-1[/tex]
a)
[tex](g\,o\,f)(x)=g(f(x))\\\\(g\,o\,f)(x)=g(x-5)\\\\(g\,o\,f)(x)=2(x-5)-1\\\\(g\,o\,f)(x)=2x-10-1\\\\(g\,o\,f)(x)=2x-11[/tex]
Invers
[tex](g\,o\,f)(x)=2x-11\\\\y=2x-11\\\\2x=y+11\\\\x=\frac{y+11}{2}\\\\(g\,o\,f)^{-1}(x)=\frac{x+11}{2}[/tex]
b)
[tex](f\,o\,g)(x)=f(g(x))\\\\(f\,o\,g)(x)=f(2x-1)\\\\(f\,o\,g)(x)=(2x-1)-5\\\\(f\,o\,g)(x)=2x-6\\[/tex]
Invers
[tex](f\,o\,g)(x)=2x-6\\\\y=2x-6\\\\2x=y+6\\\\x=\frac{y+6}{2}\\\\(f\,o\,g)^{-1}(x)=\frac{x+6}{2}[/tex]
c)
[tex](f\,o\,g)^{-1}(x)=\frac{x+6}{2}\\\\(f\,o\,g)^{-1}(3)=\frac{3+6}{2}\\\\(f\,o\,g)^{-1}(3)=\frac{9}{2}\\[/tex]
d)
[tex](g^{-1}\,o\,f^{-1})(x)=(f\,o\,g)^{-1}(x)\\\\(g^{-1}\,o\,f^{-1})(x)=\frac{x+6}{2}[/tex]
[answer.2.content]
