Question

(6Q) Find the domain and range.

Answer 1

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step 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) ∈ (-∞, ∞)