What is the range of (x+1)/(10(x-2)) ?

The range of (x+1)/(10(x-2)) is f(x) 1/10

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range of (x+1)/(10(x-2))

range

\frac{x + 1}{10 ( x - 2 )}

f (x) < \frac{1}{10} or f (x) > \frac{1}{10}

Interval Notation

(- \infty, \frac{1}{10}) \cup (\frac{1}{10}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x + 1}{10 ( x - 2 )}

Inverse of

\frac{x + 1}{10 ( x - 2 )} : \frac{1 + 20 x}{10 x - 1}

\frac{1 + 20 x}{10 x - 1}

Find the domain of each inverse function

Domain of

\frac{1 + 20 x}{10 x - 1} : x < \frac{1}{10} or x > \frac{1}{10}

Combine the intervals

f (x) < \frac{1}{10} or f (x) > \frac{1}{10}

(- 1, 2), (3, 2)

f (x) = \frac{3 x ^{2}}{x ^{2} - 4}

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

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

2 x + 3

What is the range of (x+1)/(10(x-2)) ?
The range of (x+1)/(10(x-2)) is f(x)< 1/10 \lor f(x)> 1/10