What is the domain of f(x)=(sqrt(2x+5))/(x-7) ?

The domain of f(x)=(sqrt(2x+5))/(x-7) is -5/2 7

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domain of f(x)=(sqrt(2x+5))/(x-7)

domain

f (x) = \frac{2 x + 5}{x - 7}

- \frac{5}{2} \leq x < 7 or x > 7

Interval Notation

[- \frac{5}{2}, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{5}{2}

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

- \frac{5}{2} \leq x < 7 or x > 7

(- 3, 4), (2, - 6)

f (x) = \frac{x}{9 - x ^{2}}

(- 5, - 8), (- 8, 7)

\frac{1}{4} x^{2} + \frac{2}{3} x - \frac{1}{6}

f (x) = 2 x + 7

What is the domain of f(x)=(sqrt(2x+5))/(x-7) ?
The domain of f(x)=(sqrt(2x+5))/(x-7) is -5/2 <= x<7\lor x>7