What is the range of f(x)=(x-4)/(x-5) ?

The range of f(x)=(x-4)/(x-5) is f(x) 1

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range of f(x)=(x-4)/(x-5)

range

f (x) = \frac{x - 4}{x - 5}

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x - 4}{x - 5}

Inverse of

\frac{x - 4}{x - 5} : \frac{- 4 + 5 x}{x - 1}

\frac{- 4 + 5 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{- 4 + 5 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

f (x) = \frac{10 x ^{3} + 2}{2 x ^{3}}

f (x) = \frac{( 1 - 5 t )}{( 3 + t )}

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

y = 4 x - 1

f (x) = 2 x

What is the range of f(x)=(x-4)/(x-5) ?
The range of f(x)=(x-4)/(x-5) is f(x)<1\lor f(x)>1