[tex]g-f(\frac{t}{2})=g(\frac{t}{2})-f(\frac{t}{2})[/tex]
Then, we need to substitute t=t/2 in the functions:
[tex]\begin{gathered} g(\frac{t}{2})=\frac{4t}{2}+4 \\ g(\frac{t}{2})=2t+4 \\ f(\frac{t}{2})=(\frac{t}{2})^2+2t \\ f(\frac{t}{2})=\frac{t^2}{4}+t \end{gathered}[/tex]
Subtracting the functions, would be:
[tex]\begin{gathered} (g-f)(\frac{t}{2})=(2t+4)-(\frac{t^2}{4}+t) \\ (g-f)(\frac{t}{2})=2t+4-\frac{t^2}{4}-t \\ (g-f)(\frac{t}{2})=t+4-\frac{t^2}{4} \\ To\text{ simplify a little bit, we are going to multiply (t+4) by 4 and divide by 4} \\ (g-f)(\frac{t}{2})=\frac{4t+16-t^2}{4} \end{gathered}[/tex]
