What is the domain of f(x)=sqrt(x+2)+1/(sqrt(3-x)) ?

The domain of f(x)=sqrt(x+2)+1/(sqrt(3-x)) is -2<= x<3

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domain of f(x)=sqrt(x+2)+1/(sqrt(3-x))

domain

f (x) = x + 2 + \frac{1}{3 - x}

- 2 \leq x < 3

Interval Notation

[- 2, 3)

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 2 \leq x < 3

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

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

f (x) = 3 - x + \frac{1}{x + 2}

{sin (x) : - 4 π < x < 0, 2 x : x \geq 0}

f (x) = lo g_{10} (x - 2)

What is the domain of f(x)=sqrt(x+2)+1/(sqrt(3-x)) ?
The domain of f(x)=sqrt(x+2)+1/(sqrt(3-x)) is -2<= x<3