What is the range of x/(|x-2|) ?

The range of x/(|x-2|) is f(x)>-1

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range of x/(|x-2|)

range

\frac{x}{∣ x - 2 ∣}

f (x) > - 1

Interval Notation

(- 1, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{x}{∣ x - 2 ∣} : x < 2 or x > 2

Extreme Points of

\frac{x}{∣ x - 2 ∣} :

None

Absolute value functions are piecewise functions

Find the function intervals:

x < 2, x > 2

Evaluate the function behavior for each interval

Find the range for the interval

- \infty < x < 2 : - 1 < f (x) < \infty

Find the range for the interval

2 < x < \infty : 1 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) > - 1 or f (x) > 1

f (x) > - 1

\frac{x - 3}{x ^{2} - 16}

f (x) = x^{3} - 27 x + 1

6 x - 2 y = 18

f (x) = \frac{1}{x - 4} - 2

f (x) = \frac{10}{4 - x}