https://file.aiquickdraw.com/mathbot/file/1726022064079ig6wwvhs.jpg

To solve this problem, we need to compute \( f(2) \) and \( g(0) \) from the given functions \( f(x) = x^3 + 2x - 3 \) and \( g(x) = 3x - 2 \), then subtract the results as requested: \( f(2) - g(0) \).

### Step 1: Calculate \( f(2) \)
Substitute \( x = 2 \) into the function \( f(x) \):
\[
f(2) = (2)^3 + 2(2) - 3
\]
\[
f(2) = 8 + 4 - 3 = 9
\]

### Step 2: Calculate \( g(0) \)
Substitute \( x = 0 \) into the function \( g(x) \):
\[
g(0) = 3(0) - 2 = -2
\]

### Step 3: Compute \( f(2) - g(0) \)
Now subtract \( g(0) \) from \( f(2) \):
\[
f(2) - g(0) = 9 - (-2) = 9 + 2 = 11
\]

So, the answer is:
\[
f(2) - g(0) = 11
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for practice:
1. What is \( f(1) - g(1) \) for the same functions?
2. What is the value of \( f(x) \) when \( x = -1 \)?
3. If \( g(x) = 3x - 2 \), what is \( g(2) \)?
4. How does changing the constant in \( f(x) \) from \(-3\) to \(-5\) affect the value of \( f(2) \)?
5. What would the value of \( f(x) \) be if \( f(x) = x^2 + 2x - 3 \) instead?

**Tip:** When substituting values into a function, always follow the order of operations: first calculate exponents and products, then sums or differences.

Given: f(x) = x^3 + 2x - 3 and g(x) = 3x - 2. Find: f(2) - g(0).

Explore how to calculate the difference between values of a cubic polynomial function and a linear function using given formulas. This example uses the functions f(x) = x^3 + 2x - 3 and g(x) = 3x - 2 to determine f(2) - g(0), illustrating basic function evaluation skills suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation