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Question
A function f : R → R is defined by f(x) = x2. Determine (a) range of f, (b) {x : f(x) = 4}, (c) [y: f(y) = −1].
Solution
f (x) = x2
Range of f = R+ (Set of all real numbers greater than or equal to zero)
(b) Given:
f (x) = x2
⇒ x2 = 4
⇒ x = ± 2
∴ {x : f (x) = 4 } = { -2,2} .
(c) { y : f (y) = - 1}
⇒ f (y) = - 1
It is clear that x2 = -1 but x2 ≥ 0 .
⇒ f (y) ≠ -1
∴ {y : f (y) = -1} = Φ
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