What is the domain of (log_{10}(x-2))/(sqrt(18-2x)) ?

The domain of (log_{10}(x-2))/(sqrt(18-2x)) is 2<x<9

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domain of (log_{10}(x-2))/(sqrt(18-2x))

domain

\frac{lo g _{10} ( x - 2 )}{18 - 2 x}

2 < x < 9

Interval Notation

(2, 9)

Solution steps

Find non-negative values for radicals:

x \leq 9

Find positive values for logs:

x > 2

Find undefined (singularity) points:

x = 9

Combine real regions and undefined points for final function domain

2 < x < 9

f (t) = sec (\frac{π t}{4})

f (x) = 4 x^{2} - 16

lo g_{\frac{1}{4}} (x)

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

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

What is the domain of (log_{10}(x-2))/(sqrt(18-2x)) ?
The domain of (log_{10}(x-2))/(sqrt(18-2x)) is 2<x<9