Question

Perform the indicated operation. f(t)=t²-2 g(t)=t+2 Find f(g(t))

Answer 1

To find f(g(t)) with f(t)=t²-2 and g(t)=t+2, we substitute g(t) into f(t) resulting in f(g(t)) = t² + 4t + 2.

Step-by-step explanation:

We are asked to perform the operation f(g(t)), where f(t)=t²-2 and g(t)=t+2. To solve this, we need to substitute the function g(t) into the function f(t) in place of the variable t. Here are the steps:

1. Write the function f(t) in its form, which is f(t) = t² - 2.
2. Instead of t, substitute the function g(t) = t + 2 into f(t).
3. Calculate f(g(t)) as follows:

f(g(t)) = (t + 2)² - 2

Expand the square:

f(g(t)) = t² + 4t + 4 - 2

Simplify the expression:

f(g(t)) = t² + 4t + 2