What is the range of f(x)= 4/(3+x) ?

The range of f(x)= 4/(3+x) is f(x) 0

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range of f(x)= 4/(3+x)

range

f (x) = \frac{4}{3 + x}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4}{3 + x}

Inverse of

\frac{4}{3 + x} : \frac{4}{x} - 3

\frac{4}{x} - 3

Find the domain of each inverse function

Domain of

\frac{4}{x} - 3 : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

f (x) = 16 - x^{2}

f (x) = - x^{2} - 4 x + 4

f (x) = \frac{2 x}{x + 1}

cos (x - \frac{π}{2})

f (x) = 2 x^{2} + 1

What is the range of f(x)= 4/(3+x) ?
The range of f(x)= 4/(3+x) is f(x)<0\lor f(x)>0