What is the domain of 5/((x-1)(x-4)),x\ne 1 ?

The domain of 5/((x-1)(x-4)),x\ne 1 is x 4

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domain of 5/((x-1)(x-4)),x\ne 1

domain

\frac{5}{( x - 1 ) ( x - 4 )}, x \neq = 1

x < 1 or 1 < x < 4 or x > 4

Interval Notation

(- \infty, 1) \cup (1, 4) \cup (4, \infty)

Solution steps

Set the domain to the given interval

x < 1 or x > 1

Find undefined (singularity) points:

x = 4

Join undefined points with the domain:

(x < 1 or 1 < x < 4 or x > 4) and (x < 1 or x > 1)

x < 1 or 1 < x < 4 or x > 4

y = x^{2} - 3 x - 70

f (x) = 3 - x + x + 4

f (x) = - 2 sin (2 π) x

f (x) = - 0.03 x^{\frac{1}{2}} - \frac{8}{x ^{\frac{1}{2}}}

f (X) = 205.1 X^{709.2}

What is the domain of 5/((x-1)(x-4)),x\ne 1 ?
The domain of 5/((x-1)(x-4)),x\ne 1 is x<1\lor 1<x<4\lor x>4