What is the domain of f(x)=log_{2}(3x-6)+1/(x-5) ?

The domain of f(x)=log_{2}(3x-6)+1/(x-5) is 2 5

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domain of f(x)=log_{2}(3x-6)+1/(x-5)

domain

f (x) = lo g_{2} (3 x - 6) + \frac{1}{x - 5}

2 < x < 5 or x > 5

Interval Notation

(2, 5) \cup (5, \infty)

Solution steps

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

2 < x < 5 or x > 5

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

f (x) = x^{2} + 7 x - 9

2 sin (x) + cos (2 x)

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

g (x) = \frac{2}{x + 3}

What is the domain of f(x)=log_{2}(3x-6)+1/(x-5) ?
The domain of f(x)=log_{2}(3x-6)+1/(x-5) is 2<x<5\lor x>5