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

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

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

domain

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

x < \frac{3}{4} or x > 1

Interval Notation

(- \infty, \frac{3}{4}) \cup (1, \infty)

Solution steps

Find positive values for logs:

x < \frac{3}{4} or x > 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x < \frac{3}{4} or x > 1

y = lo g_{10} (5 + 3 x)

f (x) = (2 x)^{\frac{1}{3}} - 7

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

f (x) = 2 π r^{2} + 12 π r

y = - (x + 1)^{3} + 27

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