Question

If g(t)=(3t-5)^2+4t-1, find expressions for each of the following:

Answer 1

For this case we have the following function:

$g (t) = (3t-5) ^ 2 + 4t-1$

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:

$g (a) = (3a-5) ^ 2 + 4a-1$

$g (a) = 9a ^ 2-30a + 25 + 4a-1$

$g (a) = 9a ^ 2-26a + 24$

For t = a + 2:

$g (a + 2) = (3 (a + 2) -5) ^ 2 + 4 (a + 2) -1$

$g (a + 2) = (3a + 6-5) ^ 2 + 4a + 8-1$

$g (a + 2) = (3a + 1) ^ 2 + 4a + 7$

$g (a + 2) = 9a ^ 2 + 6a + 1 + 4a + 7$

$g (a + 2) = 9a ^ 2 + 10a + 8$

Answer:

The required expressions are given by:

$g (a) = 9a ^ 2-26a + 24$

$g (a + 2) = 9a ^ 2 + 10a + 8$