What is the domain of f(x)=(x+3)/(log_{3)(9-x)} ?

The domain of f(x)=(x+3)/(log_{3)(9-x)} is x<8\lor 8<x<9

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domain of f(x)=(x+3)/(log_{3)(9-x)}

domain

f (x) = \frac{x + 3}{lo g _{3} ( 9 - x )}

x < 8 or 8 < x < 9

Interval Notation

(- \infty, 8) \cup (8, 9)

Solution steps

Find positive values for logs:

x < 9

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

x < 8 or 8 < x < 9

What is the domain of f(x)=(x+3)/(log_{3)(9-x)} ?
The domain of f(x)=(x+3)/(log_{3)(9-x)} is x<8\lor 8<x<9