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

The range of f(x)=(x^2-4)/(x^2) is f(x)<1

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

range

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

f (x) < 1

Interval Notation

(- \infty, 1)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2}

x^{2} - 4 = y x^{2}

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

Discriminant

x^{2} - 4 = y x^{2} : - 16 y + 16

- 16 y + 16 \geq 0 : y \leq 1

Check if the range interval endpoints are included

y = 1 :

Excluded

Therefore the range is

f (x) < 1

y - 27 = \frac{7}{15} (x + 12)

- 2 cos (x - \frac{π}{2})

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

f (x) = \frac{x}{x ( x - 8 )}

x^{4} - 3 x^{2}

What is the range of f(x)=(x^2-4)/(x^2) ?
The range of f(x)=(x^2-4)/(x^2) is f(x)<1