Let f : R → R : f(x) = x2.
Determine (i) range (f) (ii) {x : f(x) = 4}
Given: f(x) = x2
The graph for the given function is
(i) Range(f):
For finding the range of the given function, let y = f(x)
Therefore,
y = x2
x = √y
The value of y ≥ 0.
Hence, Range(f) is [0, ∞).
(ii) Let y = f(x) =
Given y = 4.
Therefore, =4
x = 2 or x = -2
The set of values for which y = 4 is x = {2,-2}.