What is the domain of f(x)=(12-ln(4-x))/(x-2) ?

The domain of f(x)=(12-ln(4-x))/(x-2) is x<2\lor 2<x<4

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domain of f(x)=(12-ln(4-x))/(x-2)

domain

f (x) = \frac{12 - ln ( 4 - x )}{x - 2}

x < 2 or 2 < x < 4

Interval Notation

(- \infty, 2) \cup (2, 4)

Solution steps

Find positive values for logs:

x < 4

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or 2 < x < 4

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

7 x^{2} + 2

\frac{lo g _{2} ( x - 4 )}{lo g _{2} ( 7 - x )}

f (x) = - (0.02)^{x + 6}

What is the domain of f(x)=(12-ln(4-x))/(x-2) ?
The domain of f(x)=(12-ln(4-x))/(x-2) is x<2\lor 2<x<4