(1q) find the domain and range of f(x)= 2-x + sin x

Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function

Note that f(x) is the sum of two continuous functions and

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 will be the intersection of the domains of the function and the function .

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) ∈ (-∞, ∞)