What is the range of f(x)= 1/(x-1)+1/(x-2) ?

The range of f(x)= 1/(x-1)+1/(x-2) is f(x) 0

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

range

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

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{1}{x - 1} + \frac{1}{x - 2} : \frac{3 x + 2 + x ^{2} + 4}{2 x}, \frac{3 x + 2 - x ^{2} + 4}{2 x}

\frac{3 x + 2 + x ^{2} + 4}{2 x}, \frac{3 x + 2 - x ^{2} + 4}{2 x}

Find the domain of each inverse function

Domain of

\frac{3 x + 2 + x ^{2} + 4}{2 x} : x < 0 or x > 0

Domain of

\frac{3 x + 2 - x ^{2} + 4}{2 x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

f (x) = x - 12

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

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

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

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

What is the range of f(x)= 1/(x-1)+1/(x-2) ?
The range of f(x)= 1/(x-1)+1/(x-2) is f(x)<0\lor f(x)>0