What is the domain of y=(sqrt(4x+60))/(ln(5x-40)) ?

The domain of y=(sqrt(4x+60))/(ln(5x-40)) is 8 41/5

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domain of y=(sqrt(4x+60))/(ln(5x-40))

domain

y = \frac{4 x + 60}{ln ( 5 x - 40 )}

8 < x < \frac{41}{5} or x > \frac{41}{5}

Solution steps

Find non-negative values for radicals:

x \geq - 15

Find positive values for logs:

x > 8

Find undefined (singularity) points:

x = \frac{41}{5}

Combine real regions and undefined points for final function domain

8 < x < \frac{41}{5} or x > \frac{41}{5}

∣ x ∣ - x

- 11

\frac{x ^{2} + 3 x}{x ^{2} - 16}

y = 2 - 9 - (x + 2)^{2}

f (x) = \frac{x ^{2} - 10}{x ^{2} - 4}

What is the domain of y=(sqrt(4x+60))/(ln(5x-40)) ?
The domain of y=(sqrt(4x+60))/(ln(5x-40)) is 8<x< 41/5 \lor x> 41/5