What is the range of 4/(x^2) ?

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range of 4/(x^2)

range

\frac{4}{x ^{2}}

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

\frac{4}{x ^{2}} = y

Multiply both sides by

x^{2}

4 = y x^{2}

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

Discriminant

4 = y x^{2} : 16 y

16 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{1}{x - 8}

x^{3} - 9 x^{2} + 15 x + 3

f (x) = 2^{x + 6}

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

f (x) = \frac{2}{3} x + \frac{10}{3}