What is the domain of f(x)= 3/((\frac{1){x-2})+4} ?

The domain of f(x)= 3/((\frac{1){x-2})+4} is x 2

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domain of f(x)= 3/((\frac{1){x-2})+4}

domain

f (x) = \frac{3}{( \frac{1}{x - 2} ) + 4}

x < \frac{7}{4} or \frac{7}{4} < x < 2 or x > 2

Interval Notation

(- \infty, \frac{7}{4}) \cup (\frac{7}{4}, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{7}{4}, x = 2

The function domain

x < \frac{7}{4} or \frac{7}{4} < x < 2 or x > 2

What is the domain of f(x)= 3/((\frac{1){x-2})+4} ?
The domain of f(x)= 3/((\frac{1){x-2})+4} is x< 7/4 \lor 7/4 <x<2\lor x>2