Let f : R → R : f(x) = x 2 . Determine (i) range (f) (ii) {x : f(x) = 4}

Question

Philoid · Accepted Answer

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}.