Solution
Given:
(a)
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=x-2 \\ \end{gathered}[/tex]
(1)
[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=(x-2)+2 \\ f\mleft(g\mleft(x\mright)\mright)=x-2+2 \\ f\mleft(g\mleft(x\mright)\mright)=x \end{gathered}[/tex]
(2) =
[tex]\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=(x+2)-2 \\ g(f(x))=x+2-2 \\ g(f(x))=x \end{gathered}[/tex]
(3)
[tex]\begin{gathered} For\text{ the two functions to be inverse of each other , then the condition below must be satisfied} \\ f(g(x)\text{ = g\lparen f\lparen x\rparen\rparen = x} \end{gathered}[/tex]
Thus, f and g are inverses of each other.
