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Chapter 2: Problem 7

Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1 .\) Find the following $$ f(-3) $$

Short Answer

Expert verified
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Step by step solution

01

- Identify the function to use

The problem requires the evaluation of the function \( f(x) \) at \( x = -3 \). The function given is \( f(x) = -3x + 4 \).
02

- Substitute the value of x into the function

Replace \( x \) with \( -3 \) in the function \( f(x) = -3x + 4 \). This gives: \( f(-3) = -3(-3) + 4 \).
03

- Simplify the expression

Calculate the value: \( -3(-3) \) is \( 9 \). Hence, \( f(-3) = 9 + 4 \).
04

- Final answer

Add the numbers: \( 9 + 4 = 13 \). Therefore, \( f(-3) = 13 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear functions
for functions, you replace the variable with the given value. Here's how to do it step-by-step:
1. Identify the function to use and the value to substitute. We are given the function f(x) = -3x + 4 and asked to find f(-3).
2. Replace the variable (x) with the given value. In this case, we replace x with -3:
f(-3) = -3(-3) + 4
  • 3. Perform the calculation. Multiply -3 by -3 to get 9, and then add 4:
    f(-3) = 9 + 4
  • 4. Finish up by simplifying the final result. Adding 9 and 4 gives 13:
    f(-3) = 13

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