What is the domain of f(x)=(x-7)/(x-5),x<7 ?

The domain of f(x)=(x-7)/(x-5),x<7 is x<5\lor 5<x<7

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domain of f(x)=(x-7)/(x-5),x<7

domain

f (x) = \frac{x - 7}{x - 5}, x < 7

x < 5 or 5 < x < 7

Interval Notation

(- \infty, 5) \cup (5, 7)

Solution steps

Set the domain to the given interval

x < 7

Find undefined (singularity) points:

x = 5

Join undefined points with the domain:

(x < 5 or x > 5) and x < 7

x < 5 or 5 < x < 7

7 - 4 x

f (x) = lo g_{10} (\frac{1}{2}) (4 - ∣ x ∣)

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

\frac{7}{x ( x - 5 )}

\frac{\frac{5 x ^{2}}{9}}{\frac{15 x ^{3}}{27}}

What is the domain of f(x)=(x-7)/(x-5),x<7 ?
The domain of f(x)=(x-7)/(x-5),x<7 is x<5\lor 5<x<7