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)=cos⁴ (x)-sin⁴(x) , g(x)=2 cos²(x-1)

Answer 1

To determine if the equation f(x) = g(x) is an identity, we need to graph the functions f(x) = cos⁴(x) - sin⁴(x) and g(x) = 2cos²(x-1) in the same viewing rectangle. If the graphs overlap completely or have the same shape, then the equation is an identity.

Step-by-step explanation:

To determine if the equation f(x) = g(x) is an identity, we need to graph the functions f(x) = cos⁴(x) - sin⁴(x) and g(x) = 2cos²(x-1) in the same viewing rectangle. By comparing the graphs, if the two functions are identical for all values of x, then the equation f(x) = g(x) is an identity. However, if there are any differences between the graphs, the equation is not an identity.

In this case, we can use a graphing utility to graph f(x) and g(x). Observing the graphs, if they overlap completely, or if they coincide and have the same shape, then the equation f(x) = g(x) is an identity.

On the other hand, if the graphs do not coincide or have differences at any point, then the equation f(x) = g(x) is not an identity.