Question

Let f(x) = 3x + 4 and g(x) = x² + 1.

Find the composed functions f(g(x)) and g(f(x)).
Give an example of a value for x where f(g(x)) is greater than g(f(x)). Give another example of a value for x where g(f(x)) is greater than f(g(x)).

Answer 1

To find f(g(x)), we substitute the function g(x) into f(x) and to find g(f(x)), we substitute the function f(x) into g(x). An example where f(g(x)) is greater than g(f(x)) is x = 1 and an example where g(f(x)) is greater than f(g(x)) is x = -2.

Step-by-step explanation:

To find f(g(x)), we substitute the function g(x) into f(x). So, f(g(x)) = f(x² + 1).

Substituting f(x) = 3x + 4 into g(f(x)), we get g(f(x)) = g(3x + 4).

To find an example where f(g(x)) is greater than g(f(x)), let's take x = 1.

Substituting x = 1, we have f(g(1)) = f(1² + 1) = f(2) = 10. Also, g(f(1)) = g(3(1) + 4) = g(7) = 50. Therefore, f(g(x)) > g(f(x)) for x = 1.

To find an example where g(f(x)) is greater than f(g(x)), let's take x = -2.

Substituting x = -2, we have f(g(-2)) = f((-2)² + 1) = f(5) = 19. Also, g(f(-2)) = g(3(-2) + 4) = g(-2) = 5. Therefore, g(f(x)) > f(g(x)) for x = -2.