What is the domain of f(x)=log_{2}((3-2x)/(1-x)) ?

The domain of f(x)=log_{2}((3-2x)/(1-x)) is x 3/2

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domain of f(x)=log_{2}((3-2x)/(1-x))

domain

f (x) = lo g_{2} (\frac{3 - 2 x}{1 - x})

x < 1 or x > \frac{3}{2}

Interval Notation

(- \infty, 1) \cup (\frac{3}{2}, \infty)

Solution steps

Find positive values for logs:

x < 1 or x > \frac{3}{2}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x < 1 or x > \frac{3}{2}

f (x) = \frac{7}{x ^{2} - 5}

f (x) = x^{2} - 100 x + 2650

f (x) = \frac{900 x}{10 + 45 x}

f (x) = \frac{x - 1}{x ^{2} + 5 x + 6}

y = 12 + lo g_{10} (1 - x^{2})

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