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

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

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

domain

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

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

Interval Notation

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{1}{7}

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

f (x) = x + 3 + 1

f (x) = - 6 x 5 2 x + 6

\frac{1}{7 - 3 x}

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