Math Problem Statement

Evaluating f(x) = 8 - 5x for the inputs f(4c), f(2 - k), and f(4p + 3)

Solution

To solve these problems, we need to evaluate the function f(x)=85xf(x) = 8 - 5x for each of the given inputs.

1. f(4c)f(4c)

Substitute x=4cx = 4c into the function: f(4c)=85(4c)=820cf(4c) = 8 - 5(4c) = 8 - 20c So, f(4c)=820cf(4c) = 8 - 20c.

2. f(2k)f(2 - k)

Substitute x=2kx = 2 - k into the function: f(2k)=85(2k)=810+5k=2+5kf(2 - k) = 8 - 5(2 - k) = 8 - 10 + 5k = -2 + 5k So, f(2k)=2+5kf(2 - k) = -2 + 5k.

3. f(4p+3)f(4p + 3)

Substitute x=4p+3x = 4p + 3 into the function: f(4p+3)=85(4p+3)=820p15=720pf(4p + 3) = 8 - 5(4p + 3) = 8 - 20p - 15 = -7 - 20p So, f(4p+3)=720pf(4p + 3) = -7 - 20p.

Would you like more details on any step?


Here are some related questions to deepen your understanding:

  1. How do you evaluate a function for a variable expression?
  2. What happens when the input of a function is a constant versus a variable expression?
  3. How does distributing a negative sign in expressions affect the result?
  4. Why is it important to simplify expressions after substitution?
  5. How does substituting an expression with multiple terms affect the original function?

Tip: When substituting variable expressions, remember to distribute any constants or coefficients to each term in the expression to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Function Evaluation
Algebraic Expressions
Substitution

Formulas

f(x) = 8 - 5x

Theorems

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Suitable Grade Level

Grades 8-10