The function f is defined by f x = 1 2 x + 6 . What

Choice D is correct. It’s given that the function $f$ is defined by $f\left(x\right)=\frac{1}{2}\left(x+6\right)$. Substituting $4$ for $x$ in the given function yields $f\left(4\right)=\frac{1}{2}\left(4+6\right)$, or $f\left(4\right)=5$. Therefore, the value of $f\left(4\right)$ is $5$.

Choice A is incorrect. This is the value of $2\left(4+6\right)$, not $\frac{1}{2}\left(4+6\right)$.

Choice B is incorrect. This is the value of $2+\left(4+6\right)$, not $\frac{1}{2}\left(4+6\right)$.

Choice C is incorrect. This is the value of $4+6$, not $\frac{1}{2}\left(4+6\right)$.