Question

Please Help! Evaluate the function at each specified value of the independent variable and simplify. (If an answer is undefined, enter UNDEFINED.)
g(t) = 5t^2 − 8t + 3

Answer 1

Answer:

Given:

• g(t) = 5t² − 8t + 3

Find the following

g(2)

• g(2) = 5(2²) - 8(2) + 3 = 20 - 16 + 3 = 7

g(t - 2)

• g(t - 2) = 5(t - 2)² - 8(t - 2) + 3 = 5t² - 20t + 20 - 8t + 16 + 3 = 5t² - 28t + 39

g(t) - g(2)

• g(t) - g(2) = 5t² − 8t + 3 - 7 = 5t² − 8t - 4

Answer 2

g(t)=5t^2-8t+3

$\\ \sf\longmapsto g(2)=5(2)^2-8(2)+3$

$\\ \sf\longmapsto g(2)=5(4)-16+3$

$\\ \sf\longmapsto g(2)=20-13$

$\\ \sf\longmapsto g(2)=7\checkmark$

And

$\\ \sf\longmapsto g(t-2)=5(t-2)^2-8(t-2)+3$

$\\ \sf\longmapsto g(t-2)=5(t^2-4t+4)-8t+16+3$

$\\ \sf\longmapsto g(t-2)=5t^2-20t+20-8t+19$

$\\ \sf\longmapsto g(t-2)=5t^2-28t+39\checkmark$

And

$\\ \sf\longmapsto g(t)-g(2)$

$\\ \sf\longmapsto 5t^2-8t+3-7$

$\\ \sf\longmapsto 5t^2-8t-4$