What is the range of f(x)= 3/(2x-6)+7 ?

The range of f(x)= 3/(2x-6)+7 is f(x) 7

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range of f(x)= 3/(2x-6)+7

range

f (x) = \frac{3}{2 x - 6} + 7

f (x) < 7 or f (x) > 7

Interval Notation

(- \infty, 7) \cup (7, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3}{2 x - 6} + 7

Inverse of

\frac{3}{2 x - 6} + 7 : \frac{6 x - 39}{2 ( - 7 + x )}

\frac{6 x - 39}{2 ( - 7 + x )}

Find the domain of each inverse function

Domain of

\frac{6 x - 39}{2 ( - 7 + x )} : x < 7 or x > 7

Combine the intervals

f (x) < 7 or f (x) > 7

(\frac{x}{2 x ^{2} - 5}) (x)

x^{2} + 2 x - 2

f (x) = \frac{2 x - 5}{7}

x^{3} - 8

y

What is the range of f(x)= 3/(2x-6)+7 ?
The range of f(x)= 3/(2x-6)+7 is f(x)<7\lor f(x)>7