What is the range of f(x)=3+2/x ?

The range of f(x)=3+2/x is f(x) 3

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range of f(x)=3+2/x

range

f (x) = 3 + \frac{2}{x}

f (x) < 3 or f (x) > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

3 + \frac{2}{x}

Inverse of

3 + \frac{2}{x} : \frac{2}{x - 3}

\frac{2}{x - 3}

Find the domain of each inverse function

Domain of

\frac{2}{x - 3} : x < 3 or x > 3

Combine the intervals

f (x) < 3 or f (x) > 3

y = 3 x + 2, (2, - 4)

h (x) = (x + 1) (x - 2)

6 x - y = 5, (6, 5)

2 x - y = 3

f (x) = - 3^{x + 1}