What is the range of f(x)= 1/(x-7)+4 ?

The range of f(x)= 1/(x-7)+4 is f(x) 4

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range of f(x)= 1/(x-7)+4

range

f (x) < 4 or f (x) > 4

Interval Notation

(- \infty, 4) \cup (4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x - 7} + 4

Inverse of

\frac{1}{x - 7} + 4 : \frac{7 x - 27}{x - 4}

\frac{7 x - 27}{x - 4}

Find the domain of each inverse function

Domain of

\frac{7 x - 27}{x - 4} : x < 4 or x > 4

Combine the intervals

f (x) < 4 or f (x) > 4

What is the range of f(x)= 1/(x-7)+4 ?
The range of f(x)= 1/(x-7)+4 is f(x)<4\lor f(x)>4