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

The range of f(x)= 4/(x^2) is f(x)>0

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range of f(x)= 4/(x^2)

range

f (x) = \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) = 8 x + \frac{7}{x}

f (x) = x^{2} - 64

x + 3 y = 6

f (x) = - 3 x^{2} + 34 x - 75

f (x) = \frac{x}{x + 1}