Explanation:
(g - f) means that we have to subtract f(t) from g(t)
(g - f)(t/2) means that to the resulting function from the previous operation we have to replace each t by t/2:
Let's do the first part:
[tex]\begin{gathered} g(t)-f(t)=(4t+4)-(t^2+2t) \\ g(t)-f(t)=4t+4-t^2-2t \\ g(t)-f(t)=-t^2+(4t-2t)+4 \\ g(t)-f(t)=-t^2+2t+4 \end{gathered}[/tex]
Now we have to replace t by t/2:
[tex](g-f)(\frac{t}{2})=-(\frac{t}{2})^2+2(\frac{t}{2})+4[/tex]
And we can simplify some fractions:
[tex]\begin{gathered} (g-f)(\frac{t}{2})=-\frac{t}{4}^2+\frac{2t}{2}+4 \\ (g-f)(\frac{t}{2})=-\frac{1}{4}t^2^{}+t+4 \end{gathered}[/tex]
Answer:
[tex](g-f)(\frac{t}{2})=-\frac{1}{4}t^2+t+4[/tex]
