Question
Download Solution PDFWhat is the range of the function f(x) = 1 - sinx defined on entire real line?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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].
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