Question

(6Q) Find the domain and range.

Answer 1

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Explanation:

We have the function
`f(x) = 2x + cosx`

Note that f(x) is the sum of two continuous functions
`h(x) = 2x` and
`g(x) = cosx`

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
`f(x) = h(x) + g(x)` will be the intersection of the domains of the function
`h(x) = 2x` and the function
`g(x) = cosx`.

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) ∈ (-∞, ∞)