Question

Graph f and g in the same viewing rectangle. Do the graphs suggest that the equation f(x)=g(x) is an identity? Prove your answer. f(x)=tan(x) 1+sin (x), g(x)=sin(x) cos(x) /1+sinx. Do the graphs suggest that the equation f(x) = g(x) is an identity?

Answer 1

The graphs suggest that the equation 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 analyze their behavior. Let's start by graphing f(x) = tan(x) + 1 + sin(x) and g(x) = (sin(x) * cos(x)) / (1 + sin(x)).

Upon graphing these functions and observing their behavior, we can see that the graphs intersect at some points. However, this does not necessarily mean that f(x) = g(x) is an identity. For two functions to be identical, their values must be equal for all possible values of x.

To prove that f(x) = g(x) is not an identity, we need to find at least one value of x for which f(x) is not equal to g(x). Let's evaluate both functions at x = 0. Plug in x = 0 into both f(x) and g(x) and compare the results. We find that f(0) = 1 and g(0) = 0. Therefore, f(x) is not equal to g(x) for all values of x, and the equation f(x) = g(x) is not an identity.