What is the domain of f(x)=(sqrt(2x+60))/(ln(5x-20)) ?

The domain of f(x)=(sqrt(2x+60))/(ln(5x-20)) is 4 21/5

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domain of f(x)=(sqrt(2x+60))/(ln(5x-20))

domain

f (x) = \frac{2 x + 60}{ln ( 5 x - 20 )}

4 < x < \frac{21}{5} or x > \frac{21}{5}

Interval Notation

(4, \frac{21}{5}) \cup (\frac{21}{5}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 30

Find positive values for logs:

x > 4

Find undefined (singularity) points:

x = \frac{21}{5}

Combine real regions and undefined points for final function domain

4 < x < \frac{21}{5} or x > \frac{21}{5}

2 x - 1

f (x) = x^{2} - 100

f (x) = \frac{1}{x} + 7

f (x) = lo g_{\frac{1}{2}} (x^{2} - 2 x - 15) + 7

f (x) = ln (x^{2} - 81)

What is the domain of f(x)=(sqrt(2x+60))/(ln(5x-20)) ?
The domain of f(x)=(sqrt(2x+60))/(ln(5x-20)) is 4<x< 21/5 \lor x> 21/5