What is the domain of f(x)=(sqrt(25-x^2))/(x-5) ?

The domain of f(x)=(sqrt(25-x^2))/(x-5) is -5<= x<5

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domain of f(x)=(sqrt(25-x^2))/(x-5)

domain

f (x) = \frac{25 - x ^{2}}{x - 5}

- 5 \leq x < 5

Interval Notation

[- 5, 5)

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 5 \leq x < 5

y = \frac{x - 5}{2 x - 4}

f (x) = - 2 x^{2} - 4 x

- 2 x^{2} + 3 x - 1

y = 3 x^{\frac{3}{2}} - 2 x

f (x) = lo g_{2} (x - 1) - 2

What is the domain of f(x)=(sqrt(25-x^2))/(x-5) ?
The domain of f(x)=(sqrt(25-x^2))/(x-5) is -5<= x<5