What is the domain of (2x-9)/(log_{10)(sqrt(x+3))} ?

The domain of (2x-9)/(log_{10)(sqrt(x+3))} is -3 -2

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domain of (2x-9)/(log_{10)(sqrt(x+3))}

domain

\frac{2 x - 9}{lo g _{10} ( x + 3 )}

- 3 < x < - 2 or x > - 2

Interval Notation

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

Solution steps

Find positive values for logs:

x > - 3

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 3 < x < - 2 or x > - 2

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

f (x) = \frac{x + 5}{- 3 x - 3}

\frac{x + 6}{x ^{2} + 5 x - 6}

f (x) = x 36 - x^{2}

f (x) = - 1 + 4 x - x^{2}

What is the domain of (2x-9)/(log_{10)(sqrt(x+3))} ?
The domain of (2x-9)/(log_{10)(sqrt(x+3))} is -3<x<-2\lor x>-2