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Home > CALC > Chapter 4 > Lesson 4.4.3 > Problem 4-151

4-151.
  1. Define possible functions f(x) and g(x) so that h(x) = f(g(x)). Remember f(x) ≠ x, and g(x) ≠ x. Homework Help ✎

    1. h(x) = (3x cos(x2))3

    2. h(x) = 1

    3. h(x) = x

f(x) =_____________
g(x) = cosx

One possible solution:
f(x) = x0
g(x) = x2
Find another.

One possible solution:
f(x) = x³
g(x) = 3xcos(x²)
Find another.

Recall the definition of inverse functions:
f(x) and g(x) are inverse functions if f(g(x)) = x