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}.


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