$g(x)=4 x+\frac{1}{2}$ and $h(x)=2-x$. Simplify $(g-h)(x)$

Step 1 ：Given functions: $g(x)=4 x+\frac{1}{2}$ and $h(x)=2-x$. We need to find $(g-h)(x)$

Step 2 ：Subtract h(x) from g(x): $(g-h)(x) = g(x) - h(x)$

Step 3 ：Substitute the given functions: $(g-h)(x) = (4x + \frac{1}{2}) - (2 - x)$

Step 4 ：Simplify the expression: $(g-h)(x) = 5x - 1.5$

Step 5 ：\(\boxed{(g-h)(x) = 5x - 1.5}\)