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

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

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

domain

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

- 2 < x \leq 3

Interval Notation

(- 2, 3]

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 3

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 2 < x \leq 3

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

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

f (x) = lo g_{10} (x^{2} - 4)

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

5 x - 3

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