What is the domain of 1/([\frac{1){(x-4)}]-4} ?

The domain of 1/([\frac{1){(x-4)}]-4} is x 17/4

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domain of 1/([\frac{1){(x-4)}]-4}

domain

\frac{1}{[ \frac{1}{( x - 4 )} ] - 4}

x < 4 or 4 < x < \frac{17}{4} or x > \frac{17}{4}

Interval Notation

(- \infty, 4) \cup (4, \frac{17}{4}) \cup (\frac{17}{4}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{17}{4}, x = 4

The function domain

x < 4 or 4 < x < \frac{17}{4} or x > \frac{17}{4}

What is the domain of 1/([\frac{1){(x-4)}]-4} ?
The domain of 1/([\frac{1){(x-4)}]-4} is x<4\lor 4<x< 17/4 \lor x> 17/4