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

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

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

range

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

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2}

2 = y x^{2}

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

Discriminant

2 = y x^{2} : 8 y

8 y \geq 0 : y \geq 0

Check if the range interval endpoints are included

y = 0 :

Excluded

Therefore the range is

f (x) > 0

f (x) = \frac{x ^{2}}{( x - 1 ) ^{2}}

f (x) = \frac{1}{3 - 2 x - x ^{2}}

f (x) = - 2

f (x) = x - 2 - 5