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

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

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

range

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

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x - 2}{x + 4}

Inverse of

\frac{x - 2}{x + 4} : \frac{- 2 - 4 x}{x - 1}

\frac{- 2 - 4 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{- 2 - 4 x}{x - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

f (x) = (\frac{1}{x} + 5)

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

2 + \frac{6}{x}, x > 0, y > 2

f (x) = 2 x^{3} + 6 x^{2} - 144 x + 4

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

What is the range of f(x)=(x-2)/(x+4) ?
The range of f(x)=(x-2)/(x+4) is f(x)<1\lor f(x)>1