Determine the input value for which the statement
f(x) = g(x) is true.

From the graph, the input value is approximately 
.

f(x) = 3 and g(x) = x – 2

3 = x – 2

5 = x

From your explanation, you're solving for the input value \( x \) where \( f(x) = g(x) \).

Given:
- \( f(x) = 3 \)
- \( g(x) = x - 2 \)

You correctly set \( f(x) = g(x) \), which gives the equation:
\[
3 = x - 2
\]

To solve for \( x \):
\[
3 + 2 = x
\]
\[
x = 5
\]

Thus, the input value is \( x = 5 \).

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:

1. What is the graphical interpretation of \( f(x) = g(x) \)?
2. How would the solution change if \( f(x) = 4 \) instead of \( f(x) = 3 \)?
3. Can there be more than one solution for \( f(x) = g(x) \)?
4. How would you find the solution if \( g(x) \) was a quadratic function?
5. How does shifting the graph of \( g(x) = x - 2 \) affect the solution?

**Tip:** Always check if both sides of the equation represent the same function type (linear, quadratic, etc.) to determine the possible number of solutions.

Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately . f(x) = 3 and g(x) = x – 2. 3 = x – 2. 5 = x.

Learn how to determine the input value where f(x) = g(x). This step-by-step example shows how to solve for x when f(x) = 3 and g(x) = x - 2, leading to the solution x = 5. Perfect for students in Grades 6-8 studying linear equations.

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