What is the domain of f(x)=sqrt(χ+2)+(3χ)/(2χ-1) ?

The domain of f(x)=sqrt(χ+2)+(3χ)/(2χ-1) is -2 1/2

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domain of f(x)=sqrt(χ+2)+(3χ)/(2χ-1)

domain

- 2 \leq χ < \frac{1}{2} or χ > \frac{1}{2}

Interval Notation

[- 2, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Find non-negative values for radicals:

χ \geq - 2

Find undefined (singularity) points:

χ = \frac{1}{2}

Combine real regions and undefined points for final function domain

- 2 \leq χ < \frac{1}{2} or χ > \frac{1}{2}

What is the domain of f(x)=sqrt(χ+2)+(3χ)/(2χ-1) ?
The domain of f(x)=sqrt(χ+2)+(3χ)/(2χ-1) is -2<= χ< 1/2 \lor χ> 1/2