What is the domain of y=(sqrt(5-x))/(log_{10)(x)} ?

The domain of y=(sqrt(5-x))/(log_{10)(x)} is 0<x<1\lor 1<x<= 5

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domain of y=(sqrt(5-x))/(log_{10)(x)}

domain

y = \frac{5 - x}{lo g _{10} ( x )}

0 < x < 1 or 1 < x \leq 5

Interval Notation

(0, 1) \cup (1, 5]

Solution steps

Find non-negative values for radicals:

x \leq 5

Find positive values for logs:

x > 0

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

0 < x < 1 or 1 < x \leq 5

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

f (x) = x + 1 + \frac{2 x + 3}{x + 1}

f (x) = \frac{2}{x ^{2} - 6 x + 8}

4 x^{2} - 3

f (x) = - 3 x - 6

What is the domain of y=(sqrt(5-x))/(log_{10)(x)} ?
The domain of y=(sqrt(5-x))/(log_{10)(x)} is 0<x<1\lor 1<x<= 5