Answer:
The pair one functions are given below as
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ f(g(x))=2(\frac{x}{2}+3)-6 \\ g(f(x))=\frac{2x-6}{2}+3 \end{gathered}[/tex]
Step 1:
From pair 1, substitute the value of x=1 in the
[tex]\begin{gathered} f(x)=2x-6, \\ f(1)=2(1)-6 \\ f(1)=2-6 \\ f(1)=-4 \\ \\ g(x)=\frac{x}{2}+3 \\ g(-4)=-\frac{4}{2}+3 \\ g(-4)=-2+3 \\ g(-4)=1 \end{gathered}[/tex]
Step 2:
For pair 2, substitute x=1
[tex]f(x)=7x,g(x)=-7x[/tex][tex]\begin{gathered} f(x)=7x \\ f(1)=7(1) \\ f(1)=7 \\ \\ g(x)=-7x \\ g(7)=-7(7) \\ g(7)=-49 \end{gathered}[/tex]
Step 3:
From pair one,
[tex]f(1)=-4,g(-4)=1[/tex]
From pair 2,
[tex]f(1)=7,g(7)=-49[/tex][tex]f(x)=y,g(y)=x(\text{inverse)}[/tex]
From the above conclusion, we can say that
The final answer is
PAIR 1 ONLY
OPTION B is the right answer
