What is the range of (4+5x)/(x-1) ?

The range of (4+5x)/(x-1) is f(x) 5

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range of (4+5x)/(x-1)

range

\frac{4 + 5 x}{x - 1}

f (x) < 5 or f (x) > 5

Interval Notation

(- \infty, 5) \cup (5, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4 + 5 x}{x - 1}

Inverse of

\frac{4 + 5 x}{x - 1} : \frac{4 + x}{x - 5}

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 5 or f (x) > 5

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

f (x) = (x^{2} - 5 x + 6)

sec (2 x - 1)

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

f (x) = \frac{( x + 4 )}{x ^{2} - 9}

What is the range of (4+5x)/(x-1) ?
The range of (4+5x)/(x-1) is f(x)<5\lor f(x)>5