High School

Let \( f(t) = t^2 + 5t \).

Find \( f(t - 5) \) and simplify as much as possible.

A. \( t^2 - 20t \)
B. \( t^2 - 150 \)
C. \( t^2 + 150 \)
D. \( t^2 - 5t \)

Answer :

Final answer:

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.

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.

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