Question

For each pair of functions f and g below, find f (g (x)) and g (f (x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = 2x - 3 (b) f(x) = 2x g(x) = (x + 3) / 2 g(x) = 2x f(g(x)) = f(g(x)) = g(f(x)) = g(f(x)) = f and g are inverses of each other f and g are inverses of each other f and g are not inverses of each other f and g are not inverses of each other

          For each pair of functions f and g below, find f (g (x)) and g (f (x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x) = 2x - 3
(b) f(x) = 2x
g(x) = (x + 3) / 2
g(x) = 2x
f(g(x)) =
f(g(x)) =
g(f(x)) =
g(f(x)) =
f and g are inverses of each other
f and g are inverses of each other
f and g are not inverses of each other
f and g are not inverses of each other

For each pair of functions f and g below, find f (g (x)) and g (f (x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x) = 2x - 3
(b) f(x) = 2x
g(x) = (x + 3) / 2
g(x) = 2x
f(g(x)) =
f(g(x)) =
g(f(x)) =
g(f(x)) =
f and g are inverses of each other
f and g are inverses of each other
f and g are not inverses of each other
f and g are not inverses of each other

Added by Tyler H.

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