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

We are given the function \( h(x) = 4x + 3 \), and we are asked to find \( h(4) \) and then \( h(h(4)) \).

### Step 1: Calculate \( h(4) \)
We use the function \( h(x) = 4x + 3 \) to find \( h(4) \).

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

### Step 2: Calculate \( h(h(4)) \)
Now, we know that \( h(4) = 19 \). We will substitute \( x = 19 \) into the function to calculate \( h(19) \).

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

### Final Answer
Thus, \( h(h(4)) = 79 \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. Find \( h(h(2)) \) if \( h(x) = 4x + 3 \).
2. If \( h(x) = 2x - 5 \), what is \( h(h(1)) \)?
3. Find the inverse of the function \( h(x) = 4x + 3 \).
4. Solve \( h(x) = 23 \) for \( x \) if \( h(x) = 4x + 3 \).
5. What is the value of \( h(x) \) when \( x = 0 \)?

**Tip:** When working with composite functions, always start by evaluating the innermost function first before proceeding outward.

Given h(x) = 4x + 3, find h(4) and h(h(4)).

Learn how to evaluate the function h(x) = 4x + 3, find h(4), and compute the composite function h(h(4)) step-by-step. This algebraic problem covers function evaluation and composite functions. Suitable for students in Grades 9-10.

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