Given h, of, x, equals, 4, x, plus, 3h(x)=4x+3, find h, of, 4h(4).

We are given the function \( h(x) = 4x + 3 \). You are asked to find \( h(4h(4)) \). Let's break it down step-by-step:

### Step 1: Find \( h(4) \)
Using the given function \( h(x) = 4x + 3 \), substitute \( x = 4 \):

\[
h(4) = 4(4) + 3 = 16 + 3 = 19
\]

### Step 2: Find \( h(4h(4)) \)
Now that we know \( h(4) = 19 \), we need to find \( h(19) \) by substituting \( x = 19 \) into the function \( h(x) = 4x + 3 \):

\[
h(19) = 4(19) + 3 = 76 + 3 = 79
\]

### Final Answer:
\[
h(4h(4)) = 79
\]

Would you like more details or have any questions?

Here are five related questions for further practice:
1. What is \( h(5h(5)) \) for the same function?
2. If \( h(x) = 3x + 2 \), how would you find \( h(3h(3)) \)?
3. What is the inverse of the function \( h(x) = 4x + 3 \)?
4. What is \( h(h(x)) \) for the function \( h(x) = 4x + 3 \)?
5. How does the graph of \( h(x) = 4x + 3 \) look?

**Tip:** Always check intermediate steps in a nested function like this to avoid mistakes!

Learn how to solve h(4h(4)) for the linear function h(x) = 4x + 3. This step-by-step solution demonstrates key algebraic concepts, including function evaluation and composite functions. Suitable for Grades 9-10.

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