What is the range of f(x)=(x^2-6)/(x^2) ?

The range of f(x)=(x^2-6)/(x^2) is f(x)<1

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range of f(x)=(x^2-6)/(x^2)

range

f (x) = \frac{x ^{2} - 6}{x ^{2}}

f (x) < 1

Interval Notation

(- \infty, 1)

Solution steps

Rewrite as

\frac{x ^{2} - 6}{x ^{2}} = y

Multiply both sides by

x^{2}

x^{2} - 6 = y x^{2}

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

Discriminant

x^{2} - 6 = y x^{2} : - 24 y + 24

- 24 y + 24 \geq 0 : y \leq 1

Check if the range interval endpoints are included

y = 1 :

Excluded

Therefore the range is

f (x) < 1

f (x) = \frac{1}{x + 3}

y = \frac{tan ^{2} ( 3 x ^{2} - 5 )}{( ( 4 x ^{2} - 3 x ) )}

f (t) = e^{t}

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

f (x) = 4 x^{4}

What is the range of f(x)=(x^2-6)/(x^2) ?
The range of f(x)=(x^2-6)/(x^2) is f(x)<1