Question

𝑓⁡(𝑥) =2⁢𝑥⁢
𝑔⁡(𝑥) =𝑥 +5



a. Find [𝑓∘𝑔]⁡(𝑥) and [𝑔∘𝑓]⁡(𝑥).
b. State the domain and range for each.

Answer 1

Given f(x) = 2x and g(x) = x + 5.

a)
- (f ∘ g)(x) = f(g(x)) = 2*(x + 5) = 2x + 10.
- (g ∘ f)(x) = g(f(x)) = (2x) + 5 = 2x + 5.

b) Domain and range (for each function)
- f(x) = 2x: domain = (−∞, ∞), range = (−∞, ∞).
- g(x) = x + 5: domain = (−∞, ∞), range = (−∞, ∞).
- (f ∘ g)(x) = 2x + 10: domain = (−∞, ∞), range = (−∞, ∞).
- (g ∘ f)(x) = 2x + 5: domain = (−∞, ∞), range = (−∞, ∞).