What is the range of f(x)= 3/(x^2) ?

The range of f(x)= 3/(x^2) is f(x)>0

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range of f(x)= 3/(x^2)

range

f (x) = \frac{3}{x ^{2}}

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

\frac{3}{x ^{2}} = y

Multiply both sides by

x^{2}

3 = y x^{2}

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

3 = y x^{2} : 12 y

12 y \geq 0 : y \geq 0

Check if the range interval endpoints are included

y = 0 :

Excluded

Therefore the range is

f (x) > 0