For this case we have the following function:
[tex] g (t) = (3t-5) ^ 2 + 4t-1 [/tex]
The first thing we must do for this case is to evaluate the function for different values of t.
We have then:
For t = a:
[tex] g (a) = (3a-5) ^ 2 + 4a-1 [/tex]
[tex] g (a) = 9a ^ 2-30a + 25 + 4a-1 [/tex]
[tex] g (a) = 9a ^ 2-26a + 24 [/tex]
For t = a + 2:
[tex] g (a + 2) = (3 (a + 2) -5) ^ 2 + 4 (a + 2) -1 [/tex]
[tex] g (a + 2) = (3a + 6-5) ^ 2 + 4a + 8-1 [/tex]
[tex] g (a + 2) = (3a + 1) ^ 2 + 4a + 7 [/tex]
[tex] g (a + 2) = 9a ^ 2 + 6a + 1 + 4a + 7 [/tex]
[tex] g (a + 2) = 9a ^ 2 + 10a + 8 [/tex]
Answer:
The required expressions are given by:
[tex] g (a) = 9a ^ 2-26a + 24 [/tex]
[tex] g (a + 2) = 9a ^ 2 + 10a + 8 [/tex]
