What is the range of f(x)= 4/x-5 ?

The range of f(x)= 4/x-5 is f(x) -5

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range of f(x)= 4/x-5

range

f (x) = \frac{4}{x} - 5

f (x) < - 5 or f (x) > - 5

Interval Notation

(- \infty, - 5) \cup (- 5, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4}{x} - 5

Inverse of

\frac{4}{x} - 5 : \frac{4}{x + 5}

\frac{4}{x + 5}

Find the domain of each inverse function

Domain of

\frac{4}{x + 5} : x < - 5 or x > - 5

Combine the intervals

f (x) < - 5 or f (x) > - 5

3 x - 5 x - 8

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

f (x) = \frac{x}{ln ( x - 1 )}

2 x^{2} + 7 x + 3

f (x) = 25 - x^{2}

What is the range of f(x)= 4/x-5 ?
The range of f(x)= 4/x-5 is f(x)<-5\lor f(x)>-5