What is the range of f(x)=(x-3)/(x-4) ?

The range of f(x)=(x-3)/(x-4) is f(x) 1

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range of f(x)=(x-3)/(x-4)

range

f (x) = \frac{x - 3}{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 - 3}{x - 4}

Inverse of

\frac{x - 3}{x - 4} : \frac{- 3 + 4 x}{x - 1}

\frac{- 3 + 4 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{- 3 + 4 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

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

(15.9) (3.3)

f (x) = \frac{x}{x ^{2} + 9}

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

1 + x

What is the range of f(x)=(x-3)/(x-4) ?
The range of f(x)=(x-3)/(x-4) is f(x)<1\lor f(x)>1