We have the function:
[tex]f(x)=\frac{1}{2}x-7[/tex]And want to now the value of f(-6), so we need to evaluate the function f(x) at x=-6, this means replace x by -6 in the expression of f(x), so:
[tex]\begin{gathered} f(-6)=\frac{1}{2}\cdot(-6)-7 \\ f(-6)=-\frac{6}{2}-7 \\ f(-6)=-3-7=-10 \end{gathered}[/tex]So f(-6) = -10