What is the domain of f(x)=log_{10}((x+3)/(x-2)) ?

The domain of f(x)=log_{10}((x+3)/(x-2)) is x 2

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domain of f(x)=log_{10}((x+3)/(x-2))

domain

f (x) = lo g_{10} (\frac{x + 3}{x - 2})

x < - 3 or x > 2

Interval Notation

(- \infty, - 3) \cup (2, \infty)

Solution steps

Find positive values for logs:

x < - 3 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < - 3 or x > 2

f (x) = \frac{x + 5}{7}

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

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

f (x) = x^{2} - 8 x + 18

f (x) = lo g_{2} (x + 2) - 3

What is the domain of f(x)=log_{10}((x+3)/(x-2)) ?
The domain of f(x)=log_{10}((x+3)/(x-2)) is x<-3\lor x>2