What is the range of (-4-3x)/(7x-5) ?

The range of (-4-3x)/(7x-5) is f(x) -3/7

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range of (-4-3x)/(7x-5)

range

\frac{- 4 - 3 x}{7 x - 5}

f (x) < - \frac{3}{7} or f (x) > - \frac{3}{7}

Interval Notation

(- \infty, - \frac{3}{7}) \cup (- \frac{3}{7}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 4 - 3 x}{7 x - 5}

Inverse of

\frac{- 4 - 3 x}{7 x - 5} : \frac{- 4 + 5 x}{7 x + 3}

\frac{- 4 + 5 x}{7 x + 3}

Find the domain of each inverse function

Domain of

\frac{- 4 + 5 x}{7 x + 3} : x < - \frac{3}{7} or x > - \frac{3}{7}

Combine the intervals

f (x) < - \frac{3}{7} or f (x) > - \frac{3}{7}

y = 4^{x}

(- 3, 3), (3, - 5)

f (x) = - 4 x^{2} - 4, - 5 \leq x \leq 4

f (x) = 3 x^{3} - 2

y = - 2 x + 3

What is the range of (-4-3x)/(7x-5) ?
The range of (-4-3x)/(7x-5) is f(x)<-3/7 \lor f(x)>-3/7