What is the domain of (sin(x))/(7-e^{2x-3)} ?

The domain of (sin(x))/(7-e^{2x-3)} is x (ln(7)+3)/2

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domain of (sin(x))/(7-e^{2x-3)}

domain

x < \frac{ln ( 7 ) + 3}{2} or x > \frac{ln ( 7 ) + 3}{2}

Interval Notation

(- \infty, \frac{ln ( 7 ) + 3}{2}) \cup (\frac{ln ( 7 ) + 3}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{ln ( 7 ) + 3}{2}

The function domain

x < \frac{ln ( 7 ) + 3}{2} or x > \frac{ln ( 7 ) + 3}{2}

What is the domain of (sin(x))/(7-e^{2x-3)} ?
The domain of (sin(x))/(7-e^{2x-3)} is x<(ln(7)+3)/2 \lor x>(ln(7)+3)/2