What is the domain of f(x)=log_{4}((2x+5)/(x^2)) ?

The domain of f(x)=log_{4}((2x+5)/(x^2)) is -5/2 0

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domain of f(x)=log_{4}((2x+5)/(x^2))

domain

f (x) = lo g_{4} (\frac{2 x + 5}{x ^{2}})

- \frac{5}{2} < x < 0 or x > 0

Interval Notation

(- \frac{5}{2}, 0) \cup (0, \infty)

Solution steps

Find positive values for logs:

- \frac{5}{2} < x < 0 or x > 0

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- \frac{5}{2} < x < 0 or x > 0

f (x) = \frac{7}{( 2 x - 6 ) ^{2}}

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

f (x) = ln (x^{2} + 2 x - 8)

f (x) = \frac{x + 6}{2 x - 4}

f (x) = \frac{2 x - 5}{x + 4}

What is the domain of f(x)=log_{4}((2x+5)/(x^2)) ?
The domain of f(x)=log_{4}((2x+5)/(x^2)) is -5/2 <x<0\lor x>0