Question

What is the range of the function f(x) = 1 - sinx defined on entire real line?
1. (0, 2)
2. [0, 2]
3. (-1, 1)
4. [-1, 1]

Answer 1

Correct Answer - Option 2 : [0, 2]

Concept:

The range of a function is the set of all its outputs.

Example:

Let us consider the function f: A→ B,

where f(x) = 2x and A and B = {set of natural numbers}.

Here we say A is the domain and B is the co-domain.

The set of ƒ images of all the elements of A is known as the range of ƒ.  

Calculation:

f(x) = 1 - sinx 

Here the domain of f(x) is (-∞, ∞)

At this domain, the range of sinx is [-1, 1]

Range of f(x) = 1 - sin2x = 1 - [-1, 1] 

⇒ f(x) = [0 , 2]

∴ Range of f(x) is [0 , 2].