What is the range of the function f(x) = 3x2 + 6x - 8?
Solution:
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}
Given function is:
f(x) = 3x2 + 6x - 8
= (√3x)2 + 6x - 8
= (√3x)2 + 6x + (√3)2 - (√3)2 - 8
= ((√3x)2 + √3)2 - 11
As we know, ((√3x)2 + √3)2 ≥ 0
⇒ ((√3x)2 + √3)2 - 11 ≥ -11
f(x) ≥ -11
Therefore, the range of f(x) = [-11, ∞]
What is the range of the function f(x) = 3x2 + 6x - 8?
Summary:
The range of the function f(x) = 3x2 + 6x - 8 is [-11, ∞].
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