What is the domain of f(x)= 1/(2-sqrt(8-e^{5t))} ?

The domain of f(x)= 1/(2-sqrt(8-e^{5t))} is t<(2ln(2))/5 \lor (2ln(2))/5 <t<= (3ln(2))/5

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domain of f(x)= 1/(2-sqrt(8-e^{5t))}

domain

f (x) = \frac{1}{2 - 8 - e ^{5 t}}

t < \frac{2 ln ( 2 )}{5} or \frac{2 ln ( 2 )}{5} < t \leq \frac{3 ln ( 2 )}{5}

Interval Notation

(- \infty, \frac{2 ln ( 2 )}{5}) \cup (\frac{2 ln ( 2 )}{5}, \frac{3 ln ( 2 )}{5}]

Solution steps

Find non-negative values for radicals:

t \leq \frac{3 ln ( 2 )}{5}

Find undefined (singularity) points:

t = \frac{2 ln ( 2 )}{5}

Combine real regions and undefined points for final function domain

t < \frac{2 ln ( 2 )}{5} or \frac{2 ln ( 2 )}{5} < t \leq \frac{3 ln ( 2 )}{5}

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

6 - x

f (x) = \frac{( 3 x + 2 )}{x ^{2} - 7 x}

f (x) = \frac{5}{2 5 x + 6}

f (x) = 2 x^{2} + 10 x + 1

What is the domain of f(x)= 1/(2-sqrt(8-e^{5t))} ?
The domain of f(x)= 1/(2-sqrt(8-e^{5t))} is t<(2ln(2))/5 \lor (2ln(2))/5 <t<= (3ln(2))/5