What is the range of f(x)=(-2-7x)/(3x-1) ?

The range of f(x)=(-2-7x)/(3x-1) is f(x) -7/3

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range of f(x)=(-2-7x)/(3x-1)

range

f (x) = \frac{- 2 - 7 x}{3 x - 1}

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 2 - 7 x}{3 x - 1}

Inverse of

\frac{- 2 - 7 x}{3 x - 1} : \frac{- 2 + x}{3 x + 7}

\frac{- 2 + x}{3 x + 7}

Find the domain of each inverse function

Domain of

\frac{- 2 + x}{3 x + 7} : x < - \frac{7}{3} or x > - \frac{7}{3}

Combine the intervals

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

f (x) = \frac{1 + x ^{4}}{x ^{2} - x ^{4}}

f (x) = - 2 x + 6 x^{\frac{2}{3}}

f (x) = x^{4} - 4 x^{3} + 6

f (x) = x^{3} + 3 x + 5

y = 4 x^{2}

What is the range of f(x)=(-2-7x)/(3x-1) ?
The range of f(x)=(-2-7x)/(3x-1) is f(x)<-7/3 \lor f(x)>-7/3