Question

Let f(x)=√(4-x) for x ≤ 4 and g(x) x² for all x ∈ℝ. (a) Give the domains of f+g, f g, f ∘ g and g ∘ f.

Answer 1

The domains of the functions f+g, f g, f ∘ g, and g ∘ f are x ≤ 4.

Step-by-step explanation:

The domains of the given functions can be determined by considering the restrictions on the input values based on the given conditions.

For f+g, the domain is the intersection of the domains of f and g. Since f is defined for x ≤ 4 and g is defined for all real numbers, the domain of f+g is x ≤ 4.

For f g, the domain is again the intersection of the domains of f and g. Since f is defined for x ≤ 4 and g is defined for all real numbers, the domain of f g is x ≤ 4.

For f ∘ g, or the composition of f and g, the domain is the set of input values that satisfy the conditions for both f and g. Since f is defined for x ≤ 4 and g is defined for all real numbers, the domain of f ∘ g is x ≤ 4.

For g ∘ f, the domain is the set of input values that satisfy the conditions for both f and g. Since f is defined for x ≤ 4 and g is defined for all real numbers, the domain of g ∘ f is x ≤ 4.