What is the domain of y=(log_{10}(x-3))/(sqrt(8-2x)) ?

The domain of y=(log_{10}(x-3))/(sqrt(8-2x)) is 3<x<4

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domain of y=(log_{10}(x-3))/(sqrt(8-2x))

domain

y = \frac{lo g _{10} ( x - 3 )}{8 - 2 x}

3 < x < 4

Interval Notation

(3, 4)

Solution steps

Find non-negative values for radicals:

x \leq 4

Find positive values for logs:

x > 3

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

3 < x < 4

f (x) = \frac{3}{3 x - 18}

3 x^{2} + 6 x - 9

\frac{7}{5 x - 25}

0.5

ln (8 - 2 x^{2})

What is the domain of y=(log_{10}(x-3))/(sqrt(8-2x)) ?
The domain of y=(log_{10}(x-3))/(sqrt(8-2x)) is 3<x<4