What is the range of y=1+3/(x-1) ?

The range of y=1+3/(x-1) is f(x) 1

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range of y=1+3/(x-1)

range

y = 1 + \frac{3}{x - 1}

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

\frac{x + 2}{x - 1}

Find the domain of each inverse function

Domain of

\frac{x + 2}{x - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

f (x) = x - 3 y = - 3

f (x) = x^{\frac{1}{11}} (x - 1)^{2}

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

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

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

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