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

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

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

range

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

f (x) \leq - 4 or f (x) > 0

Interval Notation

(- \infty, - 4] \cup (0, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 2 x

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

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

Discriminant

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

4 y^{2} + 16 y \geq 0 : y \leq - 4 or y \geq 0

Check if the range interval endpoints are included

y = - 4 :

Included

y = 0 :

Excluded

Therefore the range is

f (x) \leq - 4 or f (x) > 0

f (x) = 18500 (0.49 - x^{2})

(15, - 17), (- 20, - 5)

(0, 7), (- 2, - 1)

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

y = \frac{4}{x + 7}

What is the range of f(x)= 4/(x^2-2x) ?
The range of f(x)= 4/(x^2-2x) is f(x)<=-4\lor f(x)>0