We need to determine whether the functions below are inverses of each other:
[tex]\begin{gathered} f(x)=\frac{1}{2}x-10 \\ \\ g(x)=2x+5 \end{gathered}[/tex]When two functions F and G are inverses of each other, they satisfy the following result:
[tex]F(G(x))=G(F(x))=x[/tex]So, let's check whether the given functions are inverses of each other:
[tex]\begin{gathered} f(g(x))=\frac{1}{2}g(x)-10 \\ \\ f(g(x))=\frac{1}{2}(2x+5)-10 \\ \\ f(g(x))=\frac{2x}{2}+\frac{5}{2}-10 \\ \\ f(g(x))=x-\frac{15}{2} \\ \\ \Rightarrow f(g(x))\ne x \end{gathered}[/tex]Therefore, the given functions are not inverses of each other.