Question

Function operation I have the answer bad I need to do the process and I don’t know how to do it. The answer is in color red And the question is in color black

Answer 1

`g-f((t)/(2))=g((t)/(2))-f((t)/(2))`

Then, we need to substitute t=t/2 in the functions:

`\begin{gathered} g((t)/(2))=(4t)/(2)+4 \\ g((t)/(2))=2t+4 \\ f((t)/(2))=((t)/(2))^2+2t \\ f((t)/(2))=(t^2)/(4)+t \end{gathered}`

Subtracting the functions, would be:

`\begin{gathered} (g-f)((t)/(2))=(2t+4)-((t^2)/(4)+t) \\ (g-f)((t)/(2))=2t+4-(t^2)/(4)-t \\ (g-f)((t)/(2))=t+4-(t^2)/(4) \\ To\text{ simplify a little bit, we are going to multiply (t+4) by 4 and divide by 4} \\ (g-f)((t)/(2))=(4t+16-t^2)/(4) \end{gathered}`