What is the domain of f(x)=(\sqrt[4]{3x-2})/(x-5)+x ?

The domain of f(x)=(\sqrt[4]{3x-2})/(x-5)+x is 2/3 5

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domain of f(x)=(\sqrt[4]{3x-2})/(x-5)+x

domain

\frac{2}{3} \leq x < 5 or x > 5

Interval Notation

[\frac{2}{3}, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{2}{3}

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

\frac{2}{3} \leq x < 5 or x > 5

What is the domain of f(x)=(\sqrt[4]{3x-2})/(x-5)+x ?
The domain of f(x)=(\sqrt[4]{3x-2})/(x-5)+x is 2/3 <= x<5\lor x>5