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

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

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range of (x-2)/(x-4)

range

\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

y = x^{2} + 1

f (x) = 7 x - 7

x^{2} + 2 x - 3

(1, - 3), (5, - 1)

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

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