Final answer:
When graphing f(x)=(sin(x) + cos(x))^2 and g(x)=1, the graphs do not coincide, suggesting that f(x)=g(x) is not an identity.
Step-by-step explanation:
To determine if the equation f(x)=g(x) is an identity, we need to graph f(x) and g(x) in the same viewing rectangle and observe if the graphs coincide. In this case, f(x) = (sin(x) + cos(x))^2 and g(x) = 1.
We can begin by plotting the graph of f(x). Since f(x) is a squared expression, it will always be positive or zero. Therefore, the graph of f(x) will never go below the x-axis and it will have a minimum value of 0.
On the other hand, g(x) is a constant function with a value of 1. Its graph will be a horizontal line at y = 1. When we plot f(x) and g(x) in the same viewing rectangle, we see that they do not coincide. The graph of f(x) has a minimum value of 0 and it fluctuates between 0 and 2, while the graph of g(x) is a straight line at y = 1. Therefore, the graphs do not suggest that the equation f(x)=g(x) is an identity.