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

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

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

domain

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

- 1 \leq x < 3 or x > 3

Interval Notation

[- 1, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 1

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 1 \leq x < 3 or x > 3

f (x) = \frac{- 2 ( x + 2 )}{5 x ^{2} - 4 x - 9}

f (x) = - \frac{1}{2 ( 6 + x ) ^{\frac{3}{2}}}

\frac{16 - x ^{2} - 4}{2 - ∣ x - 3 ∣}

f (x) = 2 - 11 x

\frac{5 x - 6}{6 x + 1}

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