Question

Help!!

A.) show work as you evaluate the composition: (g o g) (2)

B.) show work as you find: f^-1 (x)

C.) show a composition of the two functions f and g. Are they inverse functions, explain using a complete sentence

Answer 1

Hello,

Explanation:

`A)\\g(x)=(x-5)/(-3) =(-x)/(3) +(5)/(3) \\\\(gog)(x)=g(g(x))=g((-x)/(3) +(5)/(3))\\\\=((-x)/(3) +(5)/(3) )/(3)+(5)/(3) \\\\\\=(-x)/(9) +(5)/(9) +(5)/(3)\\\\=-(x)/(9)+(20)/(9) \\\\\\(gog)(2)=-(2)/(9)+(20)/(9) =(18)/(9)=2 \\\\`

`B)\\f(x)=y=-3x-5\\exchanging\ y\ and\ x\\x=-3y-5\\3y=-x-5\\\\y=(-x)/(3) -(5)/(3) \\\\f^(-1)(x)=(-x)/(3) -(5)/(3) \\\\`

`C)\\\\(fog)(x)\ must\ be\ equal\ to\ x\\\\\\(fog)(x)=g(f(x))=g(-3x-5)\\\\=(-(-3x-5))/(3) +(5)/(3) \\\\=x+(5)/(3) +(5)/(3) \\\\\\=x+(10)/(3)\ and\ not\ x\ !!!\\`

f(x) and g(x) are not inverse functions.