What is the range of 1/(x^2) ?

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range of 1/(x^2)

range

\frac{1}{x ^{2}}

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

\frac{1}{x ^{2}} = y

Multiply both sides by

x^{2}

1 = y x^{2}

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

Discriminant

1 = y x^{2} : 4 y

4 y \geq 0 : y \geq 0

Check if the range interval endpoints are included

y = 0 :

Excluded

Therefore the range is

f (x) > 0

\frac{x ^{2} + 7 x + 1}{2 x ^{2} - 5 x - 3}

f (x) = x^{4} - 8 x^{3} + 8

2 x

f (x) = \frac{1}{6} (12 - 7 x) + 1

f (x) = 4 x^{2} + 2