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

lo g_{5} (x) + 3 lo g_{25} (x)

f (x) = \frac{x + 2}{x ^{2} - 3 x - 4}

f (x) = \frac{4}{x - 1}

f (x) = x - 4

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