Understanding the Equation Solution

To find the solution for the equation f(x) = g(x), we need to determine the points where the graphs of these two functions intersect. This is where both functions hold the same value for the same input (x).

Steps to Identify the Solution:

1. Examine the Graph: Look closely at the graph you’ve been provided. Identify all points where the line or curve representing f(x) meets the line or curve of g(x).
2. Record the Points: At each intersection point, note down the x-coordinate(s). These coordinates represent the values of x at which the functions are equal.
3. Verify the Values: As a final step, plug these x-values back into both equations to ensure that the outputs for f(x) and g(x) are indeed equal, confirming that you have found the correct solutions.

Example:

For illustration, suppose our graph shows intersections at x = 1 and x = 3.

This means f(1) = g(1) and f(3) = g(3) are the solutions to the equation f(x) = g(x).

Conclusion

By carefully examining the graph, recording the intersection points, and validating the values, you can determine the accurate solutions to the equation f(x) = g(x). Understanding the visual representation of functions and their intersections is crucial in algebra and calculus.