What is the domain of sqrt(2-x)-log_{5}(12-x^2) ?

The domain of sqrt(2-x)-log_{5}(12-x^2) is -2sqrt(3)<x<= 2

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domain of sqrt(2-x)-log_{5}(12-x^2)

domain

2 - x - lo g_{5} (12 - x^{2})

- 23 < x \leq 2

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq 2

Find positive values for logs:

- 23 < x < 23

Combine real regions and undefined points for final function domain

- 23 < x \leq 2

\frac{3 x + 1}{x}

f (x) = - \frac{16}{15} x + \frac{8}{15}

y = - 2 x - 7 + 1

f (x) = \frac{x + 7}{x ^{2} + 3 x - 4}

4 13 - 4 x

What is the domain of sqrt(2-x)-log_{5}(12-x^2) ?
The domain of sqrt(2-x)-log_{5}(12-x^2) is -2sqrt(3)<x<= 2