What is the range of (5x+9)/(4x-5) ?

The range of (5x+9)/(4x-5) is f(x) 5/4

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range of (5x+9)/(4x-5)

range

f (x) < \frac{5}{4} or f (x) > \frac{5}{4}

Interval Notation

(- \infty, \frac{5}{4}) \cup (\frac{5}{4}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{5 x + 9}{4 x - 5}

Inverse of

\frac{5 x + 9}{4 x - 5} : \frac{9 + 5 x}{4 x - 5}

\frac{9 + 5 x}{4 x - 5}

Find the domain of each inverse function

Domain of

\frac{9 + 5 x}{4 x - 5} : x < \frac{5}{4} or x > \frac{5}{4}

Combine the intervals

f (x) < \frac{5}{4} or f (x) > \frac{5}{4}

What is the range of (5x+9)/(4x-5) ?
The range of (5x+9)/(4x-5) is f(x)< 5/4 \lor f(x)> 5/4