Question

Letf(t) = t² +5t. Find f(t - 5) then simplify as much as possible.

a. t² – 20t
b. t² – 150
c. t² + 150
d. t² – 5t

Answer 1

We find f(t - 5) by substituting (t - 5) into f(t) = t² + 5t and simplifying the expression, which results in t² - 5t, option d.

Step-by-step explanation:

To find f(t - 5), we need to plug in the expression (t - 5) into the given function f(t) = t² + 5t and simplify accordingly. Let's perform this step by step:

1. First, we substitute (t - 5) for t in the function: f(t - 5) = (t - 5)² + 5(t - 5).
2. We then expand the square: f(t - 5) = t² - 10t + 25 + 5t - 25.
3. Finally, we combine like terms: f(t - 5) = t² - 5t.

Therefore, the simplified form of f(t - 5) is t² - 5t, which corresponds to option d.