What is the domain of 2/(sqrt(-x^2+4x+5)) ?

The domain of 2/(sqrt(-x^2+4x+5)) is -1<x<5

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domain of 2/(sqrt(-x^2+4x+5))

domain

\frac{2}{- x ^{2} + 4 x + 5}

- 1 < x < 5

Interval Notation

(- 1, 5)

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 5

Find undefined (singularity) points:

x = - 1, x = 5

Combine real regions and undefined points for final function domain

- 1 < x < 5

ln^{\frac{1}{x}} (x)

f (x) = 1 + x + 2

4 \cdot x + 3

f (x) = 2 + ln (x)

y = \frac{x - 7}{x + 12}

What is the domain of 2/(sqrt(-x^2+4x+5)) ?
The domain of 2/(sqrt(-x^2+4x+5)) is -1<x<5