Suppose f(x) is a twice-differentiable function which is positive and decreasing for all real numbers. Let g(x)=[f(x)]^6. For what values of x is g(x) guaranteed to be increasing?

Consider the following functions. f(x) =  1   x ,   g(x) = x2 − 4x Find  (f ∘ g)(x).         Find the domain of  (f ∘ g)(x).  (Enter your answer using interval notation.)       Find  (g ∘ f)(x).         Find the domain of  (g ∘ f)(x).  (Enter your answer using interval notation.)       Find  (f ∘ f)(x).         Find the domain of  (f ∘ f)(x).  (Enter your answer using interval notation.)       Find  (g ∘ g)(x).         Find the domain of  (g ∘ g)(x).  (Enter your answer using interval notation.)

Suppose that f and g are both odd. Which of the following functions are even? ☐ y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x) ¹3 Which of the following functions are odd? y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x)¹3

4. Determine whether the following functions are one-to-one: a) f (x) = "+1 for all real numbers x + 0 b) f (x) = for all real numbers x.