What is the range of 1/(2x-4)+1 ?

The range of 1/(2x-4)+1 is f(x) 1

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range of 1/(2x-4)+1

range

\frac{1}{2 x - 4} + 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:

\frac{1}{2 x - 4} + 1

Inverse of

\frac{1}{2 x - 4} + 1 : \frac{4 x - 3}{2 ( - 1 + x )}

\frac{4 x - 3}{2 ( - 1 + x )}

Find the domain of each inverse function

Domain of

\frac{4 x - 3}{2 ( - 1 + x )} : x < 1 or x > 1

Combine the intervals

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

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

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

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

- 2 sin (3 x + \frac{π}{2})

(2.25, 2.25), (- 1.5, 5.79)