https://file.aiquickdraw.com/mathbot/file/1727206561703uvwuu0ws.jpg

We are given two functions \( u(t) = 8t - 14 \) and \( s(t) = t^2 - 16 \). The problem asks us to find \( s(u(3)) \).

### Step-by-step solution:

1. **Find \( u(3) \)**: 
   Substitute \( t = 3 \) into the function \( u(t) \):
   \[
   u(3) = 8(3) - 14 = 24 - 14 = 10
   \]

2. **Find \( s(u(3)) = s(10) \)**:
   Now, substitute \( t = 10 \) into the function \( s(t) \):
   \[
   s(10) = 10^2 - 16 = 100 - 16 = 84
   \]

Therefore, \( s(u(3)) = 84 \).

Would you like further details on this solution or have any other questions?

Here are 5 related questions for practice:
1. What is \( s(u(2)) \) if \( u(t) = 8t - 14 \) and \( s(t) = t^2 - 16 \)?
2. What is \( s(u(0)) \) with the same functions?
3. For which value of \( t \) does \( u(t) = 0 \)?
4. If \( u(t) = 8t - 14 \), what is the inverse function \( u^{-1}(t) \)?
5. Find the composite function \( s(u(t)) \) in general form.

**Tip**: When dealing with composite functions, always work from the inside out—calculate the innermost function first!

For the functions u(t) = 8t - 14 and s(t) = t^2 - 16, what is s(u(3))?

Learn how to evaluate the composite function s(u(3)) for given functions u(t) = 8t - 14 and s(t) = t^2 - 16. This step-by-step solution covers algebraic substitution and function composition, ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation