Question

If f(x)=x^2-5x+1 , find f(t+2)

Answer 1

Given that:

`f(x)=x^2-5x+1`

Therefore:

`f(t)=t^2-5t+1`

To find f(t+2), we replace t with t+2 in f(t).

`f(t+2)=(t+2)^2-5(t+2)+1`

We can then simplify:

`\begin{gathered} f(t+2)=(t+2)^2-5(t+2)+1 \\ =(t+2)(t+2)-5t-10+1 \\ =t^2+2t+2t+4-5t-10+1 \\ =t^2-t-5 \end{gathered}`

Therefore:

`f(t+2)=t^2-t-5`