Question

In exercises 15-22, find f(g(x)) and g(f(x)).

A) Compose the functions f and g
B) Solve the equations for f and g
C) Differentiate the functions f and g
D) Evaluate the functions at specific values

Answer 1

To find f(g(x)) and g(f(x)), we substitute one function into another. For f(g(x)), substitute g(x) into f(x). For g(f(x)), substitute f(x) into g(x).

Step-by-step explanation:

To find f(g(x)), we first need to evaluate g(x) and then plug the result into f(x). To find g(f(x)), we do the opposite: evaluate f(x) first, and then plug the result into g(x). Let's use specific functions for illustration:

Let f(x) = 2x and g(x) = x^2.

To find f(g(x)), we substitute g(x) into f(x): f(g(x)) = f(x^2) = 2(x^2) = 2x^2.

To find g(f(x)), we substitute f(x) into g(x): g(f(x)) = g(2x) = (2x)^2 = 4x^2.

In general, to compose two functions f and g, substitute the inner function into the outer function.