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

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

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

domain

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

- 2 \leq x < 7 or x > 7

Interval Notation

[- 2, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

- 2 \leq x < 7 or x > 7

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

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

f (x) = \frac{x ^{2} - 4 x + 1}{x - 1}

f (x) = 3 cos (x)

f (x) = 8 - 5 x^{2}

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