What is the range of (5-2x)/(6x+3) ?

The range of (5-2x)/(6x+3) is f(x) -1/3

Popular >

range of (5-2x)/(6x+3)

range

\frac{5 - 2 x}{6 x + 3}

f (x) < - \frac{1}{3} or f (x) > - \frac{1}{3}

Interval Notation

(- \infty, - \frac{1}{3}) \cup (- \frac{1}{3}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{5 - 2 x}{6 x + 3}

Inverse of

\frac{5 - 2 x}{6 x + 3} : \frac{5 - 3 x}{2 ( 1 + 3 x )}

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < - \frac{1}{3} or f (x) > - \frac{1}{3}

4 x + 7 + 5

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

f (x) = \frac{6}{2 + e ^{x}}

f (x) = \frac{x ^{2} - x - 2}{x ^{2} - 5 x + 6}

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

What is the range of (5-2x)/(6x+3) ?
The range of (5-2x)/(6x+3) is f(x)<-1/3 \lor f(x)>-1/3