Question

How do I solve problem (B) on the attached problem?

Answer 1

Given:

(a)

`\begin{gathered} f(x)=x+2 \\ g(x)=x-2 \\ \end{gathered}`

(1)

`\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}`

(2) =

`\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=(x+2)-2 \\ g(f(x))=x+2-2 \\ g(f(x))=x \end{gathered}`

(3)

`\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}`

Thus, f and g are inverses of each other.