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

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

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

range

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

f (x) < 3 or f (x) > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 3 or f (x) > 3

f (x) = \frac{3 x ^{7} + 10}{4}

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

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

\frac{2 x + 3}{5 x - 2}

f (x) = \frac{x ^{2} - 9}{x - 1}

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