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

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

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

domain

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

- 1 < x < 3

Interval Notation

(- 1, 3)

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 3

Find undefined (singularity) points:

x = - 1, x = 3

Combine real regions and undefined points for final function domain

- 1 < x < 3

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

g (x) = x^{2} - 8 x + 12

f (x) = x (x + 13) + 40

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

f (x) = x^{3} - 12 x + 7

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