What is the range of (2x+7)/(x+2) ?

The range of (2x+7)/(x+2) is f(x) 2

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range of (2x+7)/(x+2)

range

\frac{2 x + 7}{x + 2}

f (x) < 2 or f (x) > 2

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2 x + 7}{x + 2}

Inverse of

\frac{2 x + 7}{x + 2} : \frac{7 - 2 x}{x - 2}

\frac{7 - 2 x}{x - 2}

Find the domain of each inverse function

Domain of

\frac{7 - 2 x}{x - 2} : x < 2 or x > 2

Combine the intervals

f (x) < 2 or f (x) > 2

f (x) = x - 3 + 5

4 x + 5 y = 6

y = - \frac{4}{5} cos (x)

f (x) = \frac{x ^{2} - 9}{x ^{2} + 8 x + 15}

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

What is the range of (2x+7)/(x+2) ?
The range of (2x+7)/(x+2) is f(x)<2\lor f(x)>2