What is the domain of (sqrt(2x+1))+(1/(x^2-3x-54)) ?

The domain of (sqrt(2x+1))+(1/(x^2-3x-54)) is -1/2 9

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domain of (sqrt(2x+1))+(1/(x^2-3x-54))

domain

(2 x + 1) + (\frac{1}{x ^{2} - 3 x - 54})

- \frac{1}{2} \leq x < 9 or x > 9

Interval Notation

[- \frac{1}{2}, 9) \cup (9, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{1}{2}

Find undefined (singularity) points:

x = 9, x = - 6

Combine real regions and undefined points for final function domain

- \frac{1}{2} \leq x < 9 or x > 9

What is the domain of (sqrt(2x+1))+(1/(x^2-3x-54)) ?
The domain of (sqrt(2x+1))+(1/(x^2-3x-54)) is -1/2 <= x<9\lor x>9