What is the range of f(x)=(3x-4)/(4x+9) ?

The range of f(x)=(3x-4)/(4x+9) is f(x) 3/4

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range of f(x)=(3x-4)/(4x+9)

range

f (x) = \frac{3 x - 4}{4 x + 9}

f (x) < \frac{3}{4} or f (x) > \frac{3}{4}

Interval Notation

(- \infty, \frac{3}{4}) \cup (\frac{3}{4}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3 x - 4}{4 x + 9}

Inverse of

\frac{3 x - 4}{4 x + 9} : \frac{- 4 - 9 x}{4 x - 3}

\frac{- 4 - 9 x}{4 x - 3}

Find the domain of each inverse function

Domain of

\frac{- 4 - 9 x}{4 x - 3} : x < \frac{3}{4} or x > \frac{3}{4}

Combine the intervals

f (x) < \frac{3}{4} or f (x) > \frac{3}{4}

y = - \frac{1}{2} x^{2}

f (x) = 3 + x

\frac{x ^{2} + 5 x}{x ^{2} + 7 x + 10}

f (x) = (x - 5)^{2} - 1

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

What is the range of f(x)=(3x-4)/(4x+9) ?
The range of f(x)=(3x-4)/(4x+9) is f(x)< 3/4 \lor f(x)> 3/4