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

f (x) = 5 x - 3

\frac{x ^{2} + 5}{2}

h (x) = \frac{5}{7} x^{5} - 3

f (x) = \frac{4 x ^{2} + 1}{x ^{2} - 9}

5 - (2 y + 3 x) = 7 (x - y)