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

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

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

domain

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

x < 0 or x > \frac{3}{2}

Interval Notation

(- \infty, 0) \cup (\frac{3}{2}, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > \frac{3}{2}

The function domain

x < 0 or x > \frac{3}{2}

f (x) = \frac{1955}{2 - ∣ x - 1 ∣ - ∣ x - 3 ∣}

5 + 4 x - x^{2}

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

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

What is the domain of f(x)=log_{2}(x(2x-3)) ?
The domain of f(x)=log_{2}(x(2x-3)) is x<0\lor x> 3/2