Question

Let f(x) = sin(4x) and g(x) = . Find formulas for f(g(x))

and g(f(x)).
NOTE: Enter the exact answers.
f(g(x)) =
g(f(x)) =

Answer 1

To find f(g(x)) and g(f(x)), you would generally substitute the entire function g(x) into f(x) for f(g(x)), and substitute f(x) into g(x) for g(f(x)). The exact formulas depend on the specific definition of g(x).

Step-by-step explanation:

The question seems to be missing the explicit form of the function g(x), however, assuming we have the correct formula for g(x), calculating f(g(x)) and g(f(x)) involves composing the two functions. Here's how you would generally compute the composition of two functions:

• For f(g(x)), you substitute the entirety of g(x) into the function f where f's variable x is present.
• For g(f(x)), you substitute the entirety of f(x) into the function g where g's variable x is present.

For instance, if g(x) = cos(x), then:

• f(g(x)) = sin(4 * cos(x))
• g(f(x)) = cos(sin(4 * x))

However, without the specific definition of g(x), we cannot give an exact formula.