What is the range of (1+3x)/(5-2x) ?

The range of (1+3x)/(5-2x) is f(x) -3/2

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range of (1+3x)/(5-2x)

range

\frac{1 + 3 x}{5 - 2 x}

f (x) < - \frac{3}{2} or f (x) > - \frac{3}{2}

Interval Notation

(- \infty, - \frac{3}{2}) \cup (- \frac{3}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1 + 3 x}{5 - 2 x}

Inverse of

\frac{1 + 3 x}{5 - 2 x} : - \frac{1 - 5 x}{3 + 2 x}

- \frac{1 - 5 x}{3 + 2 x}

Find the domain of each inverse function

Domain of

- \frac{1 - 5 x}{3 + 2 x} : x < - \frac{3}{2} or x > - \frac{3}{2}

Combine the intervals

f (x) < - \frac{3}{2} or f (x) > - \frac{3}{2}

\frac{x ^{8}}{x ^{4} + 7}

f (x) = x^{2} - 5, x \leq 0

3 sin (\frac{x}{π} + \frac{1}{2}) - 2

lo g_{3} (x + 2)

2 x - 3

What is the range of (1+3x)/(5-2x) ?
The range of (1+3x)/(5-2x) is f(x)<-3/2 \lor f(x)>-3/2