What is the domain of f(x)=sqrt(x+2)-log_{3}(2-x) ?

The domain of f(x)=sqrt(x+2)-log_{3}(2-x) is -2<= x<2

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domain of f(x)=sqrt(x+2)-log_{3}(2-x)

domain

f (x) = x + 2 - lo g_{3} (2 - x)

- 2 \leq x < 2

Interval Notation

[- 2, 2)

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find positive values for logs:

x < 2

Combine real regions and undefined points for final function domain

- 2 \leq x < 2

y = \frac{x + 1}{x - 1}

\frac{9}{7 x - 2}

f (x) = lo g_{10} (x) - 3

\frac{2 x - 6}{x - 4}

f (x) = 5 x + 5

What is the domain of f(x)=sqrt(x+2)-log_{3}(2-x) ?
The domain of f(x)=sqrt(x+2)-log_{3}(2-x) is -2<= x<2