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

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

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

range

y = \frac{( 5 x - 3 )}{2 x + 6}

f (x) < \frac{5}{2} or f (x) > \frac{5}{2}

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{- 3 - 6 x}{2 x - 5} : x < \frac{5}{2} or x > \frac{5}{2}

Combine the intervals

f (x) < \frac{5}{2} or f (x) > \frac{5}{2}

arccsc (x + 7)

f (x) = - 3 x + 2 - 6

\frac{x - 4}{3 x - x ^{2}}

a^{2} x + 5 y = - 3

f (x) = \frac{( 4 + 3 x )}{2 x}

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