What is the range of 1/x+1 ?

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range of 1/x+1

range

\frac{1}{x} + 1

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{1}{x} + 1

Inverse of

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

\frac{1}{x - 1}

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = - x^{2} - 2 x - 5

f (x) = lo g_{4} (x)

y = - \frac{x}{5} - 7, (3, - 9)

f (x) = \frac{x}{x ^{2} + x - 6}

8 x - 6 y = 54