What is the domain of f(x)=(x^2)/(x-1)+ln(4-|2x+1|) ?

The domain of f(x)=(x^2)/(x-1)+ln(4-|2x+1|) is -5/2 <x<1\lor 1<x< 3/2

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domain of f(x)=(x^2)/(x-1)+ln(4-|2x+1|)

domain

f (x) = \frac{x ^{2}}{x - 1} + ln (4 - ∣ 2 x + 1 ∣)

- \frac{5}{2} < x < 1 or 1 < x < \frac{3}{2}

Interval Notation

(- \frac{5}{2}, 1) \cup (1, \frac{3}{2})

Solution steps

Find positive values for logs:

- \frac{5}{2} < x < \frac{3}{2}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- \frac{5}{2} < x < 1 or 1 < x < \frac{3}{2}

f (x) = - x^{2} - 4 x - 6

f (x) = \frac{1}{\frac{4}{x - 3} - 2}

f (x) = x^{4} - 4 x^{3} + 10

\frac{x ^{2} - 2 x - 8}{x ^{2} + x - 2}

f (x) = \frac{6 x - 9}{x + 5}

What is the domain of f(x)=(x^2)/(x-1)+ln(4-|2x+1|) ?
The domain of f(x)=(x^2)/(x-1)+ln(4-|2x+1|) is -5/2 <x<1\lor 1<x< 3/2