Question

Function operation helppppg(t) = 4t+4f(t) = t^2+ 27Find (g - f)(t/2)

Answer 1

Step-by-step 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:

`\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}`

Now we have to replace t by t/2:

`(g-f)((t)/(2))=-((t)/(2))^2+2((t)/(2))+4`

And we can simplify some fractions:

`\begin{gathered} (g-f)((t)/(2))=-(t)/(4)^2+(2t)/(2)+4 \\ (g-f)((t)/(2))=-(1)/(4)t^2^{}+t+4 \end{gathered}`

Answer:

`(g-f)((t)/(2))=-(1)/(4)t^2+t+4`