Question

The following functions map mathbbR to mathbbR. Give an equation describing the composition functions g ˚ f and f ˚ g in each case.

a) g(f(x))
b) f(g(x))
c) g(f(x)) = f(g(x))
d) Equations depend on specific functions f and g.

Answer 1

To find the equations describing the composition functions g ˚ f and f ˚ g, substitute the inner function into the outer function.

Step-by-step explanation:

To find the equation describing the composition of functions g ˚ f and f ˚ g, we need to substitute the inner function of each composition into the outer function.

a) To find g(f(x)), substitute f(x) into g(x), so the equation becomes g(f(x)).

b) To find f(g(x)), substitute g(x) into f(x), so the equation becomes f(g(x)).

c) To find g(f(x)) = f(g(x)), you need specific functions f and g, which are not given in the question. Without knowing the specific functions, we cannot determine a specific equation.

d) The equations for g(f(x)) and f(g(x)) will depend on the specific functions f and g used.