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

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

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

domain

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

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}

f (x) = \frac{2 x - 9}{x - 4}

\frac{8 x + 5}{4 x + 2}

\frac{ln ( x + 5 )}{ln ( 2 )} + 3

f (x) = \frac{3 x - 1}{4 x + 1}

f (x) = \frac{2 x + 4}{x ^{2} - 5 x + 6}

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