What is the range of (x-7)/(3x-5) ?

The range of (x-7)/(3x-5) is f(x) 1/3

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range of (x-7)/(3x-5)

range

\frac{x - 7}{3 x - 5}

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{x - 7}{3 x - 5}

Inverse of

\frac{x - 7}{3 x - 5} : \frac{- 7 + 5 x}{3 x - 1}

\frac{- 7 + 5 x}{3 x - 1}

Find the domain of each inverse function

Domain of

\frac{- 7 + 5 x}{3 x - 1} : x < \frac{1}{3} or x > \frac{1}{3}

Combine the intervals

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

f (x) = 5 x^{3} - 3 x^{4}

x^{3} - 4 x

y = \frac{6}{5} cos (\frac{2 x}{7})

f (x) = 4 x^{3} - 3 x^{2} - 36 x + 17

(x - 10)^{3} + 5

What is the range of (x-7)/(3x-5) ?
The range of (x-7)/(3x-5) is f(x)< 1/3 \lor f(x)> 1/3