Math Problem Statement

If f left parenthesis x right parenthesis equals 3 x minus 3 and g left parenthesis x right parenthesis equals short dash x squared plus 4, then f left parenthesis 2 right parenthesis minus g left parenthesis short dash 2 right parenthesis = __________.

Solution

Given the functions:

  • f(x)=3x3f(x) = 3x - 3
  • g(x)=x2+4g(x) = -x^2 + 4

We need to calculate f(2)g(2)f(2) - g(-2).

Step 1: Calculate f(2)f(2)

Substitute x=2x = 2 into the function f(x)f(x): f(2)=3(2)3=63=3f(2) = 3(2) - 3 = 6 - 3 = 3

Step 2: Calculate g(2)g(-2)

Substitute x=2x = -2 into the function g(x)g(x): g(2)=(2)2+4=(4)+4=4+4=0g(-2) = -(-2)^2 + 4 = -(4) + 4 = -4 + 4 = 0

Step 3: Subtract the results

f(2)g(2)=30=3f(2) - g(-2) = 3 - 0 = 3

So, f(2)g(2)=3f(2) - g(-2) = 3.

Would you like more details or have any questions?


Here are some related questions you might find interesting:

  1. What is f(1)+g(1)f(-1) + g(1)?
  2. Find the value of f(g(x))f(g(x)) for x=1x = 1.
  3. Determine the zeros of the function f(x)f(x).
  4. What is the derivative of g(x)g(x) with respect to xx?
  5. Solve f(x)=g(x)f(x) = g(x) for xx.

Tip: When dealing with function composition or operations, carefully substitute and simplify each step to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Functions
Substitution
Arithmetic Operations

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12