Math Problem Statement

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

Solution

Given the function h(x)=4x+3h(x) = 4x + 3, we want to find h(4)h(4).

Step 1: Substitute x=4x = 4 into the function

Substituting x=4x = 4 in the function:

h(4)=44+3h(4) = 4 \cdot 4 + 3

Step 2: Simplify the expression

Now, simplify the right-hand side:

h(4)=16+3=19h(4) = 16 + 3 = 19

Therefore, the value of h(4)h(4) is:

19\boxed{19}

Would you like a detailed explanation of each step, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. What is the inverse of the function h(x)=4x+3h(x) = 4x + 3?
  2. How would you find h(h(x))h(h(x))?
  3. If h(x)=4x+3h(x) = 4x + 3, what is h(2)h(-2)?
  4. How would you determine if h(x)=4x+3h(x) = 4x + 3 is a one-to-one function?
  5. How would you graph the function h(x)=4x+3h(x) = 4x + 3?

Tip: For any function f(x)f(x), finding f(a)f(a) involves substituting aa into the function and simplifying the result.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Linear Equations

Formulas

h(x) = 4x + 3

Theorems

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Suitable Grade Level

Grades 6-8