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

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

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

range

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

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

y = \frac{1}{x}

2 x^{2} + 12 x

sec (x)

f (x) = x^{3} + 6 x^{2} + 16

(- 10, 3), (2, 8)

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