Answer: Option a.
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
We have the function [tex]f(x) = 2-x + cosx[/tex]
Note that f(x) is the sum of two continuous functions [tex]h(x) = 2-x[/tex] and [tex]g(x) =sinx[/tex]
The domain and range of h(x) are all real numbers
The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]
Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2-x[/tex] and the function [tex]g(x) = sinx[/tex].
Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)
The range of f(x) will be equal to the union of the range of g(x) and h(x)
Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)
