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

The range of f(x)= x/(x+3) is f(x) 1

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

range

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

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}{x + 3}

Inverse of

\frac{x}{x + 3} : - \frac{3 x}{x - 1}

- \frac{3 x}{x - 1}

Find the domain of each inverse function

Domain of

- \frac{3 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

y = x^{2} \cdot ln (\frac{x}{8})

(0.1) (1.4)

f (x) = \frac{x ^{2} + 4 x - 5}{x - 1}

f (x) = 7 x^{3} + 10

y = 2^{x} + 6

What is the range of f(x)= x/(x+3) ?
The range of f(x)= x/(x+3) is f(x)<1\lor f(x)>1