What is the range of f(x)=(x+2)/(x+8) ?

The range of f(x)=(x+2)/(x+8) is f(x) 1

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range of f(x)=(x+2)/(x+8)

range

f (x) = \frac{x + 2}{x + 8}

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 + 2}{x + 8}

Inverse of

\frac{x + 2}{x + 8} : \frac{2 - 8 x}{x - 1}

\frac{2 - 8 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{2 - 8 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

y = \frac{1}{2} x + 1, (1, 4)

f (x) = \frac{9}{x + 4}

2 x^{2} - 3 x + 6

f (x) = \frac{x ^{2} - 9}{x ^{2} + 4 x - 21}

- 1 - 4 cos (2 x)

What is the range of f(x)=(x+2)/(x+8) ?
The range of f(x)=(x+2)/(x+8) is f(x)<1\lor f(x)>1